I'm sure MIOBI has at least one gymnastics consultant in addition to all the knowledgable stunt doubles, so I just figure they don't listen very well. So on that note, here is a brief primer of gymnastics lingo.
Saying simply "double back" (or triple, or whatever) usually indicates a tuck position. Otherwise we'd say double pike (hips bent, legs straight), or double layout (body fully extended and straight).
Using the word double or triple always indicates the number of rotations WITHIN a single skill. I've heard a kid say in cheer-speak: "I can do a triple backhandspring." No kid, you can't, because there's no such thing. You can do three back handsprings in a row. (And the third is probably a headspring in which you will eventually break your arm, but I digress. Slapping my own wrist for gymnastics snobbery).
"Flip flop" is short for back handspring, and it's actually a term that's used. "Flic flac" is an antiquated short form of back handspring and we laugh when commentators on old videos say it.
"Flip" is slang, and a broad term; it doesn't indicate a specific skill. For instance you tell me you're gonna do a flip, but that could be a back tuck or a whipback (also called whipover--a back handspring with no hands). A coach wouldn't ever simply tell a gymnast, "Today we're working on flips."
"Salto" is the technical term for flip. All skills involving a rotation (flip) in the air with no hands, from a two-foot take off, are referred to as saltos. However, no would ever say (as a gymnast in MIOBI did one episode), "I'm working on my back salto." It's just too formal.
Disclaimer: there's always going to be some variation when it comes to regional vernacular. Heck, maybe everyone in Wyoming DOES use the term salto. But I've never met a coach from Wyoming.