I have a book with reproductions of the original sheet musicfor many of Duke's tunes. Often the original sheet music will reflect the composer's intentions, so this seemed like a good place to start. Below is a clip from the sheet music for measures 1-10 of the main theme (click to enlarge):
As is often the case, the guitar symbols do not accurately represent the harmony in the piano arrangement. For example, the Gm7 symbol in measure 2 is there only for the piano's bass note F; bar 5 could have been C7/G; bar 6 might have been better expressed as Gb7b5.
However, the way Duke actually played "It Don't Mean a Thing" follows neither the sheet music chord symbols nor the piano notes. In a number of Youtube clips, he plays mm 1-8 more like this:
| Gm | Gm | Gm | Gm G7 | C7 | F7 | Bb | Bb D7#5 |
Note (among other differences) that the sheet music resolves to Bb in bar 8, while the sequence above resolves in bar 7.
Here is a terrific live version of Ella Fitzgerald with the Ellington band:
Some fake book charts show the first 4 bars as:
| Gm | Gm#7 | Gm7 | Gm6 | (Sher New Real Book Vol. 2)
or
| Gm Gm/F# | Gm/F Gm/E | Eb7 D7 | Gm | (Hal Leonard "6th Ed." Real Book, old Real Book, Hal Leonard "Real Jazz Book")
Although these alternatives both sound good, I don't hear Duke doing either one. I don't think there's a specific required bass line or moving "My-Funny-Valentine" upper line for the string of Gm chords in bars 1-4.
The most nearly-correct printed chart I found is in the Sher New Real Book, Vol. 2. A clip of mm 1-8 is below. Aside from the moving upper voice in bars 1-4, the rest of the chart seems OK, simple and uncluttered. You might add a G7 in the last 2 beats of m4.
The Sher chart also shows two sets of alternate changes (interesting, but not "vanilla"), for mm 1-8 and for mm 5-8:
mm 1-8:
| Gm Gm/F# | Gm/F Gm/E | Eb7 D7 | G7#5 |
| Em7b5 Ebm6 | Bb6/D | C7 F7 | Bb6 (D7#5) |
mm 5-8:
| C7 C#dim7 | Bb6/D G7#5#9 | Cm7 Bmaj7 | Bb6 (D7#5) |
The bridge, by the way, is the often-used "Montgomery Ward" bridge, tweaked a little in the last 2 bars. Most charts agree on this:
| Fm7 | Bb7 | Ebmaj7 | Ebmaj7 |
| Gm7 | C7 | F7 | D7 |
Unfortunately, most charts leave off the lead-in introductory "verse," nicely performed here by Louis Armstrong:
Anyway, the bottom line is that if you are choosing a fake book chart for this song, I'd suggest the one in New Real Book Vol. 2 - pretty close to correct, and easy to work with.