What is the present participle of "stop, drop, and roll"?

Phrases are not conjugated. Only individual verbs can be conjugated. As to whether one should conjugate all three verbs in this phrase, that depends on what one wants to mean.

Since the actions denoted by the verbs (all intransitive body motion verbs with human subject) are intended to be performed in temporal sequence (i.e, first you stop, then you drop, then you roll), using a progressive can denote at most one of them, unless there is some integral name "Stop, Drop, and Roll" that's like a slogan or trademark.

Such slogans are idiomatic and subject to arbitrary grammar, which is to say either do it the way they're paying you to do it, or -- especially if nobody's paying you -- do it any way you like.