I have a book with reproductions of the original sheet music
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
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.