That's a tough question to answer, even if you did disclose what the felony was. That's because you have three hurdles to get through, and each hurdle is a separate challenge.
First, you need to be accepted into a nursing school
. Whether a school will accept a felony conviction depends on both what the conviction is and what the school's guidelines are. It is possible to get accepted...how possible, I can't tell you that, only the school can.
Second, you need to get licensed by a state BON. Keep in mind that the state BON has its own guidelines regarding criminal histories, and the fact that a nursing school accepted your criminal record doesn't mean that the BON has to accept it and license you.
Last, you need to find a job. Again, employers have their own guidelines and the fact that a BON licensed you doesn't mean that the employer has to accept your criminal record and give you a job.
The PP has the best advice: check with your school as well as the MO BON. IMO, it may be more important to check with the BON first, as it won't matter where you go to school if the state won't license you. Unfortunately, the BON may not give you a definite answer as they usually review criminal applicants on a case-by-case basis...but maybe you could at the least find out if your felony conviction is an automatic disqualification for licensure.
In addition, if you have any legal questions--and especially if you have to go in front of the BON regarding your criminal record--get a lawyer involved. The BON is NOT the nurse's friend.
Best of luck.