John Legend and Chrissy Teigen -- Our Dogs Are a Little Pee Shy

John Legend and Chrissy Teigen's dogs were a little pissed Friday at LAX ... but they had problems showing it.

The famous couple stopped at the bushes for some doggie relief following their flight ... and the flashing from the cameras knocked the pooches off kilter.

One of their pups eventually gets the job done -- but the other required more cover.