For the flute, you might be able to have the instrument made of out mithral. With such a material it would be easy to explain that it would resonate properly and still be sturdy enough to bonk people over the head with.

I'd say it'd cost about 1600 gold, 1500 for 3lbs of mithral, plus the cost of a masterwork instrument. It should be treated as both a masterwork weapon and instrument.