The paint damage over time would be dependent on the type of rubber that the flare is made of, although the paint is much less likely to be damaged than the rubber. A tape would likely be your best option and will depend on size of flare. Just to go with something that would work, I’d recommend our 3M™ Acrylic Plus Tape EX4011 product. The fender flare should be cleaned with a hexane wipe, dried, then a primer applied like 3M™ Tape Primer 94. Then wipe the fender with IPA and then adhere fender flare to fender. This would be a more permanent adhesive application, are you looking for something more removable?