5.56mm military ammo uses WC 844 powder. This is available as pulldown surplus and I've used a lot of it. I bought 100 pounds a few years ago when it was cheap and that's all I've used for 5.56.
You do need to understand this is not a cannister grade powder like most reloaders are accustomed to purchasing. Military ammo is loaded with bulk grade powders. This powder is made in large lots and each lot is tested for burning rate and velocity and pressure. The load is adjusted to yield the desired velocity and pressure. With commercial grades of powder, the powder itself is adjusted to yield the desired velocity and pressure,so every can burns at exactly the same rate and yields the sale pressure, just the opposite of what the military does.
WC 844 is an excellent powder, but if you don't want to use an unfamiliar powder, H335 will yield practically the same velocity and you can easily repeat it with each can of powder.