I am in the army and going through a divorce papers where served and signed and I want to know can I get introuble for adultrey if the army wants to

Once you obtain a legal separation its no longer adultery unless the other person is still married. As I recall, the US Armed Services do come down hard on adulterers.

You have merely served them with papers, so you are still legally married, so yes you can get in trouble with the army

Frankly I don't think the army would care.