And flamadiddle is in turn from paradiddle, which is four evenly spaced hits, LRLL or RLRR (not perfectly alternating). Pa-ra-di-ddle pa-ra-di-ddle and so forth, faster and faster, and you have a drum roll; gradually speeding that up and then slowing it down to be able to hear the individual notes, while keeping the spacing even, is something one might do in a drum audition. It's a challenge to make the left-hand and right-hand hits sound exactly the same, which is perhaps why it's "paradiddle" and not "papadiddle".

A "flam" is, as you say, hitting both sticks on the head at once, one very slightly after the other. So if you start the paradiddle with a flam instead of a single hit, it's a flamadiddle, and a doozy to play well fast.

My 1962 snare rudiments book in turn excerpts a 1934 work that uses the words "paradiddle", "flam", and "ratamacue"; but it shows the flamadiddle as a "flam paradiddle" so I guess that usage came later.

All these words are purely onomatopoeia, I think.