Actually, I’m guessing the clutch cage broke. Bikes generally have wet clutches, so it’s incredibly hard to actually burn the clutch plate. Putting too much strain on the driveline could conceivably cause the cage to fail, but there’s no way the drag of just two flags would do it, especially since (as others have pointed out already), just the strain of pushing the bike up a hill would easily exceed that.
“Bikes generally have wet clutches,...”
That’s true, but I think a Harley has a dry clutch. The transmission is separate from the engine, kind of like a car (a front wheel drive car, but with the engine crankshaft 90 degrees off from the wheel axles).