Chances of becoming an NFL kicker is based on each individual. If you can kick 60 yard field goals consistently and be extremely consistent from 50 yards in (under pressure), than you have a very good chance of becoming an nfl kicker. If you can kick touch backs almost every time as well, than you have a high chance of becoming an NFL kicker. There are multiple camps year around always looking for talented kickers (coach zauner in Arizona, loui aguiar in las vegas, are just some camps that are well know). There are also afl, ufl and cfl leagues that offer tryouts as well.. They cost about 50 bucks.
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Obviously it depends on the school, but sometimes D3 and even occasionally D2 schools are desperate to find someone who can kick. D3 schools, which are non-scholarship, would love to have a quality back-up who can simply make extra points. So, as long as you CAN kick, you can get a shot somewhere. Do not forget about NAIA schools and Junior Colleges as well.
For a punter you should try kicking the ball 40 yards or above. For a field goal you should try 30 yards or above.
Basically all footballers can kick the ball about half the length of the pitch. But some can kick it further, some goalkeepers can kick it 3/4 the length and even the length of the pitch.