Speed of Love

Say the word, I'll be there in a flash
You could say my hat is off to you
Oh, we can zoom all the way to the Moon
From this great wide wacky world
The Super Mario Players (ft. Kate Higgins) – Jump Up, Super Star! [2017] @ 0:22

Here, Higgins promises she'll be there in a flash and that she can zoom all the way to the Moon. According to the Wikipedia article on the Moon, the average distance between the Earth and the Moon is 384,402 km. According to the Wikipedia page for "flash", a camera flash usually lasts between 1/1000 to 1/200 of a second. Being conservative, we can assume Higgins here refers to the slowest flash duration, 1/200 of a second. To get to the Moon in that time, she'd require a speed of 276,771,211,336 km/h (that's almost 277 billion kilometers per hour), which is roughly 256 times the speed of light in a vacuum (1,079,252,848.8 km/h).
Don't get me wrong, but how are you going to get back home?
Oh, I'd be willing to walk that way
There's something I've just got to say
I could walk a million miles today
The Wedding Present - A Million Miles [1987] @ 1:45

In this piece David Gedge says he is willing to walk a million miles (1,609,344 km) until the end of the current day – today. Thus, if Gedge is singing at precisely midnight, that gives him 24 hours to travel that distance. That requires a speed of 67,056 km/h, about 1⅔ of Earth's escape velocity (40,270 km/h).
I'll drive a million miles
To be with you tonight
Wang Chung – Everybody Have Fun Tonight [1986] @ 0:26

In the song, Wang Chung promises to drive one million miles until tonight. According to the Wikipedia page on "Night" , the night is considered to start around 8 pm and to last to about 4 am. Thus, if they are singing at one second past 4 am, that would give them 24 hours to drive said thousand miles, requiring a speed of at least 67,056 km/h, which is roughly twice the orbital speed of Saturn around the Sun (34,848 km/h), according to the Wikipedia page on Saturn.

Sadly, although travelling at the same speed, the Wang Chung mustn't get the same praise as Gedge, seeing as the latter promises to walk instead of drive.
I drove all night to get to you
Is that all right?
Roy Orbison - I Drove All Night [1992] @ 0:44

To estimate a speed for Orbison in this song, we must first estabilish where he was "driving all night". The song "I Drove All Night" was written and composed by Billy Steinberg and Tom Kelly. According to their Wikipedia pages, they both seem to have lived most of their lives in California, USA. According to the Wikipedia article on "Speed limits in the US", the speed limit on an urban freeway in California is between 80–105 km/h. Assuming Orbison was very eager to reach his destination, we can place his top speed at about 105 km/h.
'Cause you know I'd walk a thousand miles
If I could just see you tonight
Vanessa Carlton – A Thousand Miles [2001] @ 1:11

Carlton promises to walk a thousand miles (1,609.344 km) until tonight. Considering the night to start around 8 pm and to last to about 4 am, if Carlton is singing at precisely 4 am and one second, she has a full 24 hours to walk said miles. That puts her minimum speed at 67.056 km/h, which is nearly the top speed of a Kangaroo (70 km/h), according to the Wikipedia article on the Kangaroo.
If you need me, call me; no matter where you are
No matter how far, don't worry baby
Just call my name, I'll be there in a hurry
Marvin Gaye & Tammi Terrell – Ain't No Mountain High Enough [1967] @ 0:16

In this piece, Terrel suggests that regardless of distance, she will rush to reach whatever destination her lover currently is. However, since there is no clear speed defined in this excerpt, we are required to fetch another section of the lyrics, that says:

If you ever need a helping hand
I'll be there on the double
Just as fast as I can
@ 1:44

Here, Gaye and Terrel promise that they will travel as fast as [they] can. The fastest manned aircraft was the X-15, that reached a record speed of 7,274 km/h. However, taking into account the very low availability of X-15's in the current aircraft market, for the purposes of this study we are considering Gaye and Terrel refer to the fastest speed they can reach by foot.

According to the Wikipedia article on "Footspeed", the fastest human footspeed ever recorded was 44.72 km/h. Assuming Gaye and Terrel are human beings, yet disconsidering any rest periods, we can set that speed as a limit to how fast they can travel there.
Well, I must've walked a hundred miles or more
I went to every store in town
Buck Owens – Christmas Shopping [1968] @ 1:20

Owens doesn't specify any time duration in the song, but we can assume that, considering he went Christmas shopping, he must've walked while stores were open. According to the Wikipedia page on "Shopping hours", typical store shopping hours in the US (Owen's home country) are Monday - Saturday (9:00 to 22:00). If we consider Owens started his walk at 9 am and ended it at 10 pm, that gives him a total of 13 hours to walk his alleged 100 miles (160.9344 km). That puts his speed at around 12.3796 km/h, or at about half the speed of an elephant (24.9 km/h), according to the Wikipedia article on "Fastest animals".

Although Owens technically isn't singing about meeting a loved one, he is singing to a loved one about his beloved children, so this song was included in the ranking.
A thousand miles seems pretty far
But they've got planes and trains and cars
I'd walk to you if I had no other way
Plain White T's – Hey There Delilah [2005] @ 2:02

Unlike Carlton, here Plain White T's initially considers alternatives to walking, although eventually comitting to going by foot in case said alternatives are unavailable. Furthermore, there doesn't seem to be any time limit set, unless one considers the following line as an arriving date:

Two more years and you'll be done with school
@ 2:39

Assuming it will take 2 years for Plain White T's to cover the promised distance, that translates to a speed of approximately 0.092 km/h, which is about twice the speed of a garden snail (0.047 km/h), according to the Wikipedia page on the garden snail.

I could fly a thousand oceans
But there's nothing that compares to
What we had and so I walk alone
5 Seconds of Summer – Wherever You Are [2013] @ 1:19

Here, 5 Seconds of Summer say they are willing to fly a thousand oceans. The greatest stretch of ocean on Earth is on the Pacific Ocean, measuring about 19,800 km, from Indonesia to the coast of Colombia, according to the Wikipedia article on the Pacific Ocean. Therefore, they promise to fly at most about 19,800,000 km, or roughly 14 times the diameter of the Sun (1,391,016 km), according to the Wikipedia page on the Sun .

However, there is no set speed defined, and thus they might take an eternity to accomplish this feat. Moreover, their motivation isn't to see a loved one; instead, to their partner they only promise thoughts and an urge to call:

But I just can't stop thinking of you
Wherever you are
You
Wherever you are
Every night I almost call you
just to say it always will be you
Wherever you are
@ 0:45
I'd go the whole wide world (2x)
Just to find her
I'd go the whole wide world (2x)
To find out where they hide her
Wreckless Eric – Whole Wide World [1977] @ 0:55

We can trace a path from the southernmost part of South America, passing through North America, then over to Asia, southbound to Oceania, then heading northwest to Europe, then finally going south to Africa. This way, one could cover most continents (the whole wide world) and find a loved one. The total distance traveled following this path, using a very conservative estimate, would be between 50,000 and 70,000 km.

However, as great hitchhiking as this sounds, Eric doesn't specify at what speed he will be travelling at, thus invalidating the entire promise.
I'm going away
But I'll be back
Though I go 10,000 miles
Mary Chapin Carpenter – 10,000 Miles [1999] @ 0:46

In this song, Carpenter promises to, presumably, walk an astonishing 10 thousand miles (which translates to 16,093.44 km, close to Earth's diameter, 12,742 km). However, she does not define a time limit to cover that distance and, therefore, might take a lifetime to deliver on the promise.
I walk ten thousand miles,
Ten thousand miles to see you
Ally Kerr – The Sore Feet Song [2004] @ 0:14

Like Mary Chapin Carpenter, in this song Kerr promises to walk a whopping 10 thousand miles (about the distance from New York to Sydney, 9,945 km). But since there is no set timeframe, we cannot confidently estabilish a speed for her.

Kerr does at one point say Every single night and day…, hinting that it took her multiple days walking. Sadly, that is just not enough information to pin down her velocity.
But I would walk 500 miles
And I would walk 500 more
Just to be the man who walks a thousand miles
To fall down at your door
The Proclaimers – I'm Gonna Be (500 Miles) [1988] @ 0:36

The Proclaimers here claim that they would walk 500 miles (804.672 km), and then another 500 miles – possibly with a break in between. However, since there isn't a timeframe specified, this could potentially take a lifetime to be executed, rendering the promise virtually meaningless.