Without judging whether it appropriate, I think the reason someone might use two flats in the key signature is the
Eb7 chord of the vamp and the
E flat at the end of the first part of the melody...
...could be considered to come from the Phrygian mode rather than tritone substitution/altered dominant harmony.
If a tritone substitute is considered clearly identifiable only when part of a descending fifth progression, then it seems reasonable to say the
Eb7 chord here is not a tritone substitution, but a chord rooted on the lowered second degree of Phrygian.
In other words
iim7b5 bII7 i would be a clear case of tritone substitution,
bII subs for
V, because it substitutes in a progression of three roots by descending fifth. But just alternating
bII7 i bII7 i is not the clear substitution within a descending fifths progression pattern.
So, if someone took that view - the
Eb7 is not a tritone substitution - the chord is diatonic to Phrygian (at least the base triad), the Phrygian key signature reinforces that idea.
When the tune gets to using a dominant rooted on
A at end the phrase, and it has a proper leading tone, that doesn't contradict Phrygian, not in the classical sense, so that seems like additional support for Phrygian.
Either way it doesn't change what's happening tonally. It's a little like when Baroque scores would use zero flats for
D minor. The sharps and flats in the score make the final determination of tonality.