Swivel breech rifles have long held a great fascination for me too. As a result, I have studied the images of original rifles in all of the books I can procure, as well as handled some originals and contemporary examples at Dixon's Gunmaker's Fair.
I'd hazard a guess, and say they originated in Germany. At least, that seems to be the birthplace of most of the original European rifles I've studied. Having two barrels, I also think it can be said that they are heavier than a soldier would want to carry, and too, more costly than a common man could afford. So military use as an issue rifle is out. I would be surprised though if some of them here in North America did not see martial employment. A fair number of original swivel breeched rifles have survived and are in collections. That may be partly because they were of more value than a common single barreled arm, and so were better cared for. But that's speculation and supposition, as is most of my rambling.
Most of the flint era rifles appear to have a trigger guard latch, ei: the for'd section of the guard moves rearward to allow the barrels to be rotated. On some original percussion rifles, there is a pin for'd of the guard that is pulled rearward to accomplish this. On another percussion rifle, there is a button on the breech tang that is depressed to release the barrel's for rotation. I saw an original at a gun show many years ago that had a very simple plate that rotated vertically in the tang to unlatch the barrels. Nicholas Hawk, who made some wonderfully decorative swivel breech rifles and some plain ones too, used a latch that involved pulling the entire trigger guard rearward as a barrel latch. Dave Waters has written a well illustrated book (for sale in the commercial forum) a copy of which resides in my library, that features a side lever opposite the lock to disengage the barrels. So whatever device you can imagine is probably correct, as it seems they've all been tried before.
I intend to build the Wm. Antes swivel breech rifle, and to that end, I've procured two .54 cal John Getz barrels, a lovely piece of English walnut, the correct butt plate and I've made a guard based on another of his longrifles, as the guard on the swivel rifle is missing. I have all of the lock parts for the two flint actions and will make the plate and internals myself. Also, I've made preliminary drawings of the action, preparatory to diving in to the build.
But I've got some obligations to deal with first, so it's a future project, and one I continue to revel in. If you're looking for examples of good contemporary work, Mark Wheland built a wonderful Bonewitz rifle a few years ago, and whose pictures were posted here. Also, a Berks Co. rifle by Randy Steffy if you can find his pictures - a grand rifle.