A jazz blues in F is a very common type of tune in jazz. The chord progressions are basic, but are not very easy to play over because there are a lot of harmonic possibilities and often the tempo is high.
| I7 | IV7 | I7 | |
| IV7 | #IVdim | I7 |(II V) |
| II | V |(II V) | II V |
This blues is in the key of F.
You can't get away here by playing the F blues scale all the time, you'll sound boring and out of tune in some places. The F blues scale sounds good on the I and even better on the IV.
On the I you can play the F Mixolydian mode. Adding blue notes (sliding from ab to a natural for example) will sound nice and relevant :)
On the IV play Bb Mixolydian. Guitar position-wise it might be easier to think F Dorian here and stay in the same position.
On the #IV diminished chord you can play a B diminished scale (whole - half). The F blues scale works good as well here.
On the II V to Gm, you can play the G harmonic minor scale. You can play the C altered scale on C7 for variation.