I know there's a Yamaha shop on Nha Chung street (search for "La Restaurant" on the site - it's pretty much across the street from there). I don't remember if they have flutes or not, but it seems a reputable place.

This place has all kinds of brass instruments. Its easy to find on the same road as St Joseph's Church just walk from there up to Hang Bong Street and its on the left.

When I was in there I didn't ask about price, but nothing was labelled with a price.