It sounds like you're asking not about how to ensure that you never own a gun, but rather how to make sure that no one else uses your identity to own a gun.
If that's the case, part of the trouble you're going to encounter is in the patchwork of laws around the country. In different states, there are different things that would disqualify you from owning a gun. Just "going to jail" would not be enough anywhere in the country.
At the federal level, though, 18 U.S.C. § 922(d) prohibits gun sales to:
- felons and people under indictment for a felony;
- people who unlawfully use or are addicted to drugs prohibited by the Controlled Substances Act;
- illegal aliens;
- people adjudicated mentally defective;
- people committed to a mental institution;
- people who have been dishonorably discharged from the military;
- former U.S. citizens who have renounced their citizenship;
- people subject to court order restraining them from harassing or threatening a family member or intimate partner; and
- people convicted of misdemeanor domestic violence.
So if you satisfy any of those criteria, no one's allowed to sell a gun to you. Of course, only some of those are actually knowable to the public in a way that would get you on the FBI's list so that you'd show up when someone runs a background check.
So if you want to really get yourself on a list, you could get yourself convicted of a felony, but that seems like a pretty steep price to pay to prevent the highly unlikely possibility of someone using your identity to purchase a gun.