Hey @Alexey_Kruchenok, thanks for asking! Since the feature was requested before, it’s not unreasonable to see if we can add support for this in Tiled for everybody.
The problem is of course that there are already 3 bits reserved for flipping, but that they are not enough for hexagonal tiles. This is mostly since they are not just for rotation, but actually mean flipping along various axis (x, y and x+y). This way, for orthogonal maps not just rotation in 90-degree steps is achieved but also flipping either horizontally or vertically.
Now, it actually never makes sense to flip a hexagonal tile along the x+y axis. It would turn a pointy topped hex into a flat topped hex and vica-versa. So maybe we could instead say that this bit means “rotate 60” for hex maps. Unfortunately, then we’re still 4 combinations short:
So I we’d need another bit for 120 degree rotation for example, if we wanted to support both rotation and flipping on hexagonal maps. I do think it would be nice to support this, and I could certainly try to help you add the feature in a way that it can be merged.