Can a NY felony conviction prevent you from being a volunteer firefighter?

Questioner does not give his state of residence. All firefighters must be certified by some kind of state body established for certifying emergency service personnel. Such a record may disqualify you in one jurisdiction but perhaps not in another. ALSO - since Volunteer Fire Companies are usually independent entities, some volunteer departments may choose to not hire someone with a criminal record. Suggest you contact the VFD you are interested in or your state certifying agency and simply ask.