A couple of questions Ken,
What rate of vat are you paying?
Are you asking for the relevant charity to reclaim the vat or the commercial operator acting on behalf of the charity?
I ask as I once worked at a police ASU that helped out an air ambulance with (free) fuel when the local SAR flight couldn't help. This then became a bit of a habit until it was pointed out that we didn't pay vat on our fuel so couldn't give it away to a party liable for vat (however we might want to!) and that the recipient of the tax payers generosity was in fact a commercial operator acting on behalf of the charity, but possibly not passing on the 'free' fuel to the charity....
Good luck with your quest, if the airlines don't pay it why should a charity AOC.