Dating from one of the wars of the last century, a recommendation to "explode brown" is a request to stuff a grenade up your own ass and pull the pin.
"Harry, you worthlessgit! When are you going to explode brown and save the Jerries, or your own men (should they be so brave), the trouble of putting you out of our collective miseries?"
Short-hand for the word floccinaucinihilipilification, meaning the estimation of something as valueless (encountered mainly as an example of one of the longest words in the English language).