Don't know why flat-base bullets would be a pain to load in properly chamfered brass.
H322 and, especially, H4198 are classic powders in the .222, and 8208 and TAC work pretty well with heavier bullets. But I recently tried those plus some newer powders as well, and LT-30 was the clear accuracy winners with lighter bullets, and LT-32 with 50-55 grain bullets.