In the NFL, it is illegal to kick a loose ball.
ARTICLE 2. ILLEGALLY KICKING BALL
No player may deliberately kick a loose ball or a ball that is in a player’s possession.
Penalty: For illegally kicking the ball: Loss of 10 yards. If the foul is by Team A before possession changes during a scrimmage down: Loss of down and loss of 10 yards except for a foul by Team A beyond the line of scrimmage during a scrimmage kick, in which case there is no loss of down.
Some notes from the same ruling:
If a loose ball is unintentionally touched by any part of a player’s leg (including the knee), it is not considered kicking and is treated as touching.
The ball is not dead when an illegally kicked ball is recovered, unless another rule prescribes otherwise.
To answer your followup, if the kick is intentional, then it will be a penalty, and no touchdown would be granted (unless the penalty were declined). If the kick is deemed unintentional, then it will be recoverable (and would be a touchdown if recovered in the end zone by the opposing team).