Although I have a factory fluted barrel ( .22/250 ), I've never had one fluted. The Handi's have pretty meaty barrels, I'm sure it would be fine. I've read where some folks don't like to flute and existing barrel, they prefer to flute the blank, before it is bored and rifled, but a while back I visited BenchMark barrels, who make truly fine barrels, and they fluted an existing, otherwise finished barrel, so I guess if it is good enough for them, well, it's good enough for me.
One the other hand, Wayne York, who does considerable re-chambering for us Handi folks, does not like to do it, so there is the other side of the coin. I see an add often in one of the Woilfe publishing mags ( Rifle? Handloader? ) who offers fluting. I'm at work, so no info available on him, right now.
Mark