I thought the hazard lights were the brake lamps not the tail lamps, is it the tail lamp fuse that blows or the brake lamp fuse?
The only reason the fuse will blow is if there is a higher amp draw than the fuse is rated for. There must be a draw on the circuit other than that of the four lamps. Either a short to ground somewhere or the hazard circuit is short circuited into another circuit such as the tail lights, or perhaps the hazard switch or flasher itself is drawing too much.
Any short to ground downstream from the lamps will not blow the fuse but a short upstream from the lamps will.
Check the lamps and the lamp sockets for corrosion.
The hazard circuit also involves the front marker so the problem could be there.