Yep, looks like the clear coat has started to become brittle and flake off. Had the same issue with my spoiler. It can happen on occasion, even on the higher quality, more expensive spoilers.
The correct way to fix it is to remove and sand the entire spoiler. You want to remove all of the original/old clear coat and create a nice clean/smooth surface for the next/new coat of clear. Then, apply a new coat of clear over everything (except for the underside of the spoiler). This is a big PITA (pain in the ass), especially if you do not have the proper tools or the experience with sanding auto body panels. Yes, you can always take a short-cut and simply apply clear coat to only the affected areas. However, the result/appearance may not look good (i.e. you’ll probably be able to feel and see where the newer clear coat was applied). Also, once you get some delamination/flaking of the clear, it will likely get worse and spread to other parts of your spoiler. So, if you choose to do just spot repairs, you’ll likely find yourself needing to repeat the spot treatment on another/different area a few months later when you get/see additional flaking on other parts of your spoiler.
So, I suggest simply replacing the spoiler with a new one. This is what I did with mine. Here is a link to another thread where I discussed how I removed & replaced my spoiler. Good luck!!
Post in thread 'Removing a rear spoiler from PPF?'
Removing a rear spoiler from PPF?