Jazz French Horn player...I have similar problems. Just pester, pester, pester. Ask bands straight out if they'd take you on, volunteer to transpose sax parts or trumpet parts (which should be generally within range) or even write out your own from score. Emphasise that you want to do it rather than asking if you can, if that makes sense - they'll respond much better to "I'm a jazz flautist and really interested in joining, I'll transpose, I'll write out my own parts if necessary" than "do you have flute parts and do you take flautists on?" The other option is if you have a second instrument already, go on that and then mention you'd like to see how flute sounds on a couple of tunes. (Obviously if you don't play something else already, this probably won't work).
Also, if you ever fancy coming down to
NYJO by train, they have flute parts and I know they're looking for flautists (especially if you can improvise). I've been going since mid-September and it's fab. Bit of a trek from Doncaster, but then again there's someone there who comes down every few weeks from Cardiff!
Hope that helps a bit