First determine if the paint on the bumper is OEM or refinish. If its refinish it needs to come off for best longevity. If it's OEM that's great. leave it on because it will be an excellent base for what you are going to do. Sounds like bumper has been repainted if it is peeling as that is a red flag. Because of that (peeling) I would also try to determine if it is an OEM bumper or an aftermarket one. If it is aftermarket I would see about returning it. Only reason to buy a bumper from a salvage yard is to get an OEM one. Doing all the work that is required to fix it is kinda pointless on a aftermarket one. Borderline on a OEM one when you consider what you can a quality aftermarket one for.
Irregardless if it is peeling that means it is refinish and it needs to come off. There are plastic specific paint strippers available SEM is a good choice. Either of these two work OK.
XXX Bumper Stripper is an aerosol material designed to safely remove refinish materials from flexible parts.
www.semproducts.com
Urethane Bumper Stripper safely removes refinish materials from flexible parts.
www.semproducts.com
Or you can sand/blow it off. Most of the time even when using stripper you will have to sand the cover to get it all off. It can be painstaking and time consuming. If it is OEM paint underneath you want to leave that. Urethane stripper is designed to only remove the refinish paint. Not the OEM as that is the best base to start with.
So after you get the paint off, you can sand light scratches/gouges out of the cover without any filler. Deeper gouges, most body shops just use conventional glaze. In thin coats it works pretty good. Yes it will crack if flexed to much but if you hit something that flexes it that much there is going to be other damage anyway.
I've generally only repaired bumper covers the Collision Repair way which is to fill defects on the plastic directly then prime. If you have the time a better way would be to sand and expose the gouges trying to feather them out slightly and remove any fuzzy plastic, then adhesion promoter on all the bare plastic and then epoxy. After epoxy has set up for the required time 24 hours (min) -48 hours (better) then apply your choice of either conventional glaze or a bumper specific product like UPOL Stronghold. Get everything corrected then re-prime with epoxy after applying adhesion promoter again over any bare plastic areas exposed during the sanding process. Sand the primer until it's ready for paint just like you would a metal panel.
Never use anything coarser than 180 grit during the entire process.
No need for any flex additive in your clear. If you use epoxy for your primer it will help with minimizing any cracking. But again generally you only get cracking if you bump or hit something.
Ask more questions if you have them.