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A kick is a kick is a kick
NF 2-23-2: "A kick ends when a player gains possession or when the ball becomes dead while not in player possession."
Blocks, muffs, none of these things matter - it's still a kick until either someone picks it up or the ball becomes dead.
6-2-2 & 6-2-3 tell us that anyone can catch, recover, and advance the ball in or behind the expanded neutral zone.
Once the ball crosses the expanded neutral zone, though, it is treated in all respects like a normal punt.
If K is the first to touch the ball after it crosses, then it is first touching, and R will be able to take the ball at that spot. If R is first to touch, then the ball is fair game, and K will get the ball at the point of their recovery.
Other rule references:
6-2-4 & 6-2-5 detail what happens when K touches a scrimmage kick downfield. 5-1-3f & 5-1-3g tell us who gets the new series awarded.
Here are your rule references for not throwing a flag:
NF 9-7-2 tells us: "No player shall bat a loose ball other than a pass or a fumble in flight, or a low scrimmage kick in flight which he is attempting to block in or behind the expanded neutral zone." This tells us that the block of the kick is legal.
NF 2-2 defines batting: "Batting is intentionally slapping or striking the ball with the arm or hand." You describe muffs, defined in 2-26: "A muff is the touching or accidental kicking of a loose ball by a player in an unsuccessful attempt to secure possession." Muffing a loose ball is not a foul.
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