LR has advantages in filtration, grazing and overall habitat for the fish. But it is not absolutely necessary if you have something like a wet/dry or other area for lots of bacteria.
Basically when cycling you want an ammonia source. If cycling with damsels, for example, you should still be feeding very heavily so excess food also breaks down. Or you can throw coctail shrimp in. Or you can used uncured LR. Or you could use pure ammonia. Many possibilities. But yes, you can use flake food or whatever. May just cause a bit more of a clean up (bit messier). This is why some cocktail shrimp from the grocery store are often preferred.