Key of Eb

Verse, starts at (0:07)

1 - 5of4 - 4 - 4
4 - 3 - 6 - 6
2 - 5 - 5of4 - 5of4
4 - 3 - 6 - 6
2 - 5 - 1 - 1   ....

Eb - Eb/Db - Ab - Ab
Ab - Gm - Cm - Cm
Fm - Bb - Ebsus - Ebsus
Ab - Gm - Cm - Cm
Fm - Bb - Eb - Eb ....

First 5of4 is the second main chord once the band comes in. It is an Eb7 but with it's b7 in the bass (so a 7bass chord), can easily be played as an Eb triad with Db in the bass (Eb/Db)

The second 5of4 (at 0:25) is played as super sus, so Eb with just 1-b7-2-4 (or whatever order you want). Very common voicing for a 5of4. 

Key of G

Verse, starts around 0:10

6 - 5of4 - 4 - 5of6

Em - G7 - C - B7

Wildly typical of this style. In fact, Tom Misch does literally the same thing below, what are the odds!

Everything is pretty normal, except for the final B7 which is initally played as Bsus4, then B7. Some other fun things are happening in the second half of the verse, but that's for another discussion!

Key of D

Main loop

6 - 5of4 - 4 - 5of6

Bm - D7 - G - F#7

Wildly typical of this style. A few things to note:

All of the chords are thicker voicings, like:

Bm is more Bm9 or even Bsus (like B-F#-A-C#)

D7 is Dsus (super sus, extremely common for a 5 of 4).

G has all of the maj7 type flavors so an added 7 or 2.

F#7 starts as normal dominant with a 6, then spicy with b6 (so F#7b6 or F#7#5, or F#aug7). Sometimes also starts as an F#supersus or even a C#min9, which yields the same sound.

Later in the song they start replacing the G (4) with Em (2), an easy move as you are simply replacing a major chord with it's relative minor.