What would you call a person who farts a lot?

Solution 1:

Further to Thusagen's answer, the single word would be flatulent.

Solution 2:

This person, in medicine, would have been called, "someone suffering from excessive flatulence"

Solution 3:

The French performer Le Pétomane, was a professional flatulist, who was known by several terms:

• Flatulist
• Fartiste
• Farteur

From Wikipedia (linked above):

Le Pétomane (/ləˈpɛtəmeɪn/, French pronunciation: ​[ləpetɔˈman]) was the stage name of the French flatulist (professional farter) and entertainer Joseph Pujol (June 1, 1857 – 1945). He was famous for his remarkable control of the abdominal muscles, which enabled him to seemingly fart at will. His stage name combines the French verb péter, "to fart" with the -mane, "-maniac" suffix, which translates to "fartomaniac". The profession is also referred to as "flatulist", "farteur", or "fartiste".1

Solution 4:

I personally call such a person a fart-machine. ;)

But the correct term is flatulent.