I claim no special knowledge about this. I personally do not know anybody who has done this, so this is my thinking only. Take it for what it’s worth. Anyway, to adress your question:
A Congressman, while being a party to a declaration of war and its related funding, is not a part of the chain of command. The President is. Therefore, Congressmen create no conflict, but the President potentially would.
Perhaps you’re speaking of the speech limitations placed on members of the military? To me that presents no obvious conflict if you’re a) not on a military status, b) do not represent yourself as a spokesman for the military (which is why public speaking in uniform at rallies and such is verboten, because it tends to lend an air of false authority), and c) do not do anything to discredit the chain of command.
That last is the hardest part. How do you run for higher office without taking shots at the policies of the incumbent? In politics, nice guys really do finish last, but one good shot at the President could cost you. In the Guard you are mostly subject to the state version of the UCMJ (here called the Pennsylvania Code of Military Justice) which is comparatively painless, but a person in the Reserves is subject to the UCMJ at all times, and that has teeth.
This relates to me indirectly. Because of my username I have had to show more discretion that I would have otherwise for fear that I bring discredit publicly to my service. In other words, I have had to show much more discretion than I perhaps would have with any other random name. The Internet is just as real as anywhere else, and it could conceivably come back to bite me.