When the hazard lights are turned on they blink a few times and then the tail light fuse blows. Any ideas why? Suggestions for trouble shooting?

Is the tail light fuse the correct amperage?

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.

If Tail lights and Brake lights work normally before trying Hazards, I would suspect the hazard relay or the column switch. You can move your turn signal relay to the hazard spot on the fuse block easily enough to rule that out first. I hope its not the column switch (I just swapped mine out because my hazard connector was broke off) and its not that simple to do.

I like the idea your tail light fuse is just to low a value as well.

Blowing 20A fuses in the Stop/Haz slot of the fuse box. Tail lights and brake lights work fine. I tried switching the hazard relay with the turn signal relay and still blew fuses. Maybe the switch? When I activate the switch the hazard lights blink a couple times and then the fuse blows.

Do your front park/marker lights work OK?

most likely grounding out some where, look for wire with rubbed off rubber coating...