Darn, oh well, you're probably right. After all, given her attachment to the flute, I bet she would be holding on to it pretty tightly. And she's already shown that she won't be bossed around by Dee; she wouldn't leave without her flute just because Dee was telling her to hurry up. Thanks for looking into that Zeph.
And Zosimus I agree with you as well, Michael probably would have specifically mentioned her losing her flute. I don't see any reason why he would've kept it a secret
So I guess it's not completely impossible that she lost the flute, just not very likely.