I'd go back to the double sided tape but use the right one.

I use 3M Body Moulding tape for just about everything. It is designed specifically for body mouldings and if both surfaces are cleaned with metho, you'll have a hard time getting the flares off again. The best part is it sticks instantly - no waiting for anything to go off.

It is available from most automotive paint suppliers at about $15 a roll. (My last roll lasted me 10 years!)