Kicking team can't advance ANY kick (kickoff, punt, try or FG) unless it's a scrimmage kick that has not crossed the neutral zone. The kick ends when it is possessed by either team or is otherwise dead by rule. So if the receiving team possesses it and then fumbles it, it's no longer a kick and recovery by the kicking team allows them to advance it. If a punt or FG or try is blocked and the kicking team recovers it before it crosses the neutral zone, they can advance it.
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