Even if there was wallpaper previously, you have to remove the peeling paint, because it will “shield” any primer/sealer from adhering to the substrate.
*** I hate to say it, but sand the flaky stuff off the walls, using a drywall sanding screen.
*** Rinse off the sanding dust well, and any wallpaper glue. When that’s DRY…
*** Use the Shellac-based primer from Zinsser. It’s kinda smelly, but the best product for this use. You can’t clean this stuff off a roller, so just toss it…BUT use top-quality equipment though!!!
*** Now your ready for TWO coats of (preferably) Semi-gloss paint.
*** Follow these steps and you should get a great result.
Thanks!
Faron