What I am going to say may sound complicated, but it really isn't. Practically anything will work. The only real rule is to not feed them Layer until they are ready to lay. The extra calcium can cause kidney damage or bone deformation to a growing chick. Notice that I said "can", not that it absolutely will. And they will not immediately fall over dead the instant they eat a bite of Layer. It is a cumulative effect, causing damage eating it over time. And sometimes you don't notice the damage. A chicken falls over dead a year or more later for no apparent reason. Those damaged kidneys finally gave out.
One progression is to feed Starter (usually around 22% protein around here, but it can vary) until they are 4 to 8 weeks old, then switch to a 16% Grower. Different manufacturers give different recommendations, but it really doesn't matter. Whenever the bag of feed is finished after 4 weeks, switch to Grower. Then, when they start to lay or they hit 20 weeks, switch to Layer. You don't have to switch to Layer at 20 weeks if they are not laying, but you can. The general idea is that they need a higher protein feed to help them get a good start to life, but after a while, they don't really need the higher protein feed. Let their physical growth slow down a bit to match their maturity and the development of their internal organs.
Some people switch to a 15% Grower/Finisher at about 13 weeks, then switch to Layer later. Further to the thought that they don't need the higher protein at this stage.
Some people feed a 20% combined Starter/Grower from day 1 until they switch to layer. They don't need the higher protein, but it really doesn't hurt them.
Some people feed a 20% Flock Raiser the whole time, until they switch to Layer. This is formulated a little different that the Starter/Grower, but not much different. It is more intended for flocks where some will be meat chickens and some will be egg layers. It is also real handy for people raising turkeys or such that need the higher protein with their chickens.
Some people never switch to Layer. Instead, they offer oyster shell on the side and feed Grower or Flock Raiser. The ones that need the extra calcium for egg laying get it and the rest do not eat more calcium than they need. This is extremely logical if you have a mixed age flock.
I do stay away from the high protein game bird feed for the flock. I think it really does have more protein that is good for them if fed over an extended period of time. A few weeks on this should not hurt them, but I do think that too much of a good thing is not necessarily a good thing. Their liver does have to work harder to get that extra protein out of their system.
I think you have a whole lot of options, but I would not use the Layer yet.
