I have  sterling silver dragonfly brooch but the enamelling on the wings is  partly chipped and cracked . How can I remove this and is it possible to   re enamel it again ?

Yes the enamel can removed and enameled again. If this is an heirloom take to a professional since it sounds like you don't enamel. If it's a nice keepsake you could try to repair with colored resin. Make color test samples on a paperplate to compare to the original colors. Either add the resin to the piece on top of the enamel or use a diamond burr in your flex shaft to remove the old enamel.

If it is heirloom the enamel may be lead based and you sure wouldn't want that dust flying around from grinding out with a diamond bur unless done underwater. I don't do enamel so I not sure what the correct method would be but that just doesn't sound right. Where's Edmund when you need him? He would know the answer for sure.