What's the best way to get those staples out of the fender skirt and the new ones in when replacing the rubber flaps?

Don -

If you do a search on "splash shield" you should see a ton of posts, including pictures.

If you want to try to reuse the staples, you carefully unbend /open them up and pull them out. Same thing if you are not reusing them, you can just get a little more vigorous unbending them.

In your search results, you'll see most of us throw the replacment staples away and use stainless wire because it's easier to work with.