wikipedia suggests that Barracks Lawyer is the more common term in the US Army:
"Barracks Lawyer —someone who claims to know all the regulations and UCMJ by heart and threatens to use them against the chain-of-command regularly; similar to a "jailhouse lawyer" or a "shithouse lawyer"

It's not clear from that that shithouse lawyer is also used in the army, or just a term we are all supposed to know.

http://en.wikipedia.org/wiki/User:Offrdk5/List_of_U.S._Army_acronyms_and_expressions

However, something called wiktionary states pretty clearly that shithouse lawyer is a US equivalent to UK Barracks Lawyer or Sea Lawyer:

Sea Lawyer
(US Navy, Coast Guard, RN) A sailor, probably too smart for his own good, who thinks he knows all of the regulations and quotes them to get out of either work or trouble. Other US and UK military equivalent is "Barrack Room Lawyer" (UK), and "Barracks Lawyer" or, more crudely, "Shithouse Lawyer" (US).

(What did you learn on mudcat today, dear?)