If the mud flaps molds around the fenders and covers some paint, definitely. The Mabbet mudflaps I have on do not cover any painted surfaces so those are staying on.
The Air Design instruction says to only apply it to the built in channel under where the tape is. Debris can still get under the flares similar to these that way. Best to just apply it all around the perimeter.
Just want to share my short experience with fender flares with everyone: they will accumulate dust/debri, and possibly salt underneath that could potentially cause rust issues later on.
I decided to install the Mabbet flares on mine to keep rock chips off around the wheels as I drive on...