You can still get a flight from Kiev to Baku with Buta (who are the low cost arm of Azal Air) on 10th June for less than £100 with a hold bag. It leaves at 12.30. Problem is getting to Kiev to connect that flight. One possibility some friends were pondering was via LViv in the Ukraine. Buta announced that they had opened a twice weekly flight on Monday/Thursday starting in December but I can only see prices announced until the end of March. Ryanair/Wizz fly there direct on the 10th for about £60 so might be worth contacting Buta to see if a connection works and/or when fares are released.

Good luck. Baku's a good place to visit and cheap as chips (Euro 2020 mark-ups not withstanding) when you get there.