The only way the team would get to kick it again is if the ball does not cross the line of scrimmage such as like was mentioned earlier - if it's a bobbled snap, etc. In that situation the kicking team could fall on it and re-kick. Also if the ball is blocked and recovered by the kicking team they could re-kick it. Once the ball crosses the line of scrimmage it results in a change of possession unless one of the defensive players pulls a "Leon Lett" and touches the ball downfield and it's recovered by the kicking team.
“If there are no animals in Heaven, then when I die I want to go where they went.” - Will Rogers (paraphrased)