it's probably too late but i just did a similar thing with butterflies. I made a butterfly, animated it with shapekeys, changed the min & max values of the keys to -1 & 1, then i added a keyframe for the shapekey on frame 0 (you do not care about the value). In the graph editor i added a 'sinus' modifier on the key value and voila, the butterfly move the wings in a loop. The magic thing with this method is that you can now use the butterfly as a particle, the loop wont be sync for all the butterflies since the movement of the wings is not hardcoded but calculated. (i think)

Only one butterfly & only one particle system, but many many variations...

I didn't tested it, but if it works for shapekeys values, it should also work for bones rotations, or translations.

Now i'm trying to make them landed at start and fly away when a dummy come close to them...

It's probably too late but I just did a similar thing with butterflies. I made a butterfly, animated it with shapekeys, changed the min & max values of the keys to -1 & 1, then I added a keyframe for the shapekey on frame 0 (you do not care about the value). In the graph editor I added a 'sinus' modifier on the key value and voilà, the butterfly moves the wings in a loop. The magic thing with this method is that you can now use the butterfly as a particle, the loop won't be sync for all the butterflies since the movement of the wings is not hardcoded but calculated (I think).

Only one butterfly & only one particle system, but many many variations...

I didn't tested it, but if it works for shapekey values, it should also work for bone rotations, or translations.

Now I'm trying to make them landed at start and fly away when a dummy comes close to them...