You wouldn't get a proper seal around the anuses...ani? whatever, the cornholes. So the combined farts would escape out through some path between the cheeks.

Now, for science, if you were to surgically seal the two butts together, in some sort of inverse human centipede, the fart with more force would overcome the other fart and both farts would enter the other anus. Unless they were evenly matched in force, then the farts would build in pressure in the cavity between the anusssies, until both were breached and created one long uninterrupted tube from mouth to mouth. Just as god intended.

Again, this would be done for scientific research only...