First answer:
No, the military will not find out about your affiliation unless you tell them. The
Church of Satan does not report membership to the FBI or any organization for that matter, and therefore membership would not be apparent in a background screen.
Second Answer: The military can do nothing at all if you are a member of the
Church of Satan. I personally filled out government documents listing my affiliation willingly, and not only was there no fuss from officers, but no flak from other applicants who viewed my tattoo. In short, the military in my experience is not as anti-Satanic as some seem to think.
Third Answer: There are military Satanists on this message board, quite a few of them actually. While it is up to them to reveal themselves for contact with you, perhaps you will find useful counseling through them.
Ever forward, and my appreciation for your service as a citizen.