As long as your vision can be corrected to 20/20 with glasses or contacts, you will be eligible for a First Class FAA Medical Certificate, which makes you eligible to fly as a civilian professional pilot. This is much less restrictive than military pilot vision requirements.
Felony convictions can prevent you from becoming a pilot and/or remaining a pilot once you’ve completed training. The FAA has even refused to issue medical certificates for student pilots because of felony drug convictions. Substance abuse and being branded a security threat are common reasons for FAA denial. Although felons are not strictly barred from becoming pilots, the FAA has leeway in denying licensing. Good moral character is an expected character trait of pilots. If you are unsure about your felony conviction, contact the FAA.