I think you will have that problem no matter what foundation you use, the pigment just gets caught in the flaky bits. I have the same issue with really dry flaky cheeks and also underneath and between my eyes and eyebrows. It depends on what kind of finish you are after but here are my favourites that i think look the best that you can get in chemists:
Bourjois healthy mix
Revlon colorstay (dry combo) - applied with a damp sponge
Rimmel match perfection
Sponging rather than buffing with brushes also works better for me with most foundations as it adds a bit of moisture to kind of flatten the dry bits. Buffing just tends to push the foundation under and around the flakey bits which makes them even more highlighted
My all time favourite is YSL touche eclat which i know isn't cheap by any means but i think it's worth it as it's just perfect for me in coverage and texture
My favourite concealer is the one by OCC which isn't too bad a price considering it lasts a good long while as it's so pigmented. It's nicely emollient.It is difficult to get of over here though which is a bit of a bummer.
If you have to powder any areas like i have to do with my nose and chin sometimes and also to set my concealer my absolute fave is the loreal BB powder it makes your skin look like an amazing piece of perfect velvet.
Using a flannel to wash your face with also helps. As much as I now hate Caroline Hirons she was right on that point.
Sorry for going on so much but i hope it helps!