Illegal kick
 

I was LJ today when this situation happened 80 feet in front of me:

On a kickoff from K40, K's kicker almost completely whiffs and the ball barely rolls off the kicking tee. He looks at it confused for a moment, two teammates run to try to recover it, but he then kicks it again after the ball has traveled about 3 inches. This second kick travels about 5 yards, for a grand total of about 5 yards, 3 inches, and K recovers at its own 45 while R is scratching their heads.

Our result of the play: First touching by K at the K40, then K45 yard line. Kick recovered by K.

Our penalty: illegal kicking by K at the 40 yard line. It was accepted by R, 1st and 10 R at the K25.

I'm soliciting comments on our handling of this situation. If you need more details, let me know and I'll see what I can remember.

Result of the play: right, so R would have the option of declining the penalty and taking the ball at the spot of first touching.

Penalty: Check that again. Why would K lose the opportunity to replay the down?

If you were a LJ in OH (5-man) this would have taken place 60 YARDS away from you. ;)

If R accepts the foul, K is rekicking from the K-25.

There best option is to decline and take the ball at the first touching spot.

The choice of spots is interesting, but I'd say the main issue is whether you're sure the ball was actually moved from its spot by contact with the kicker's foot. If he hit it so badly that it was displaced only 3", it'd be with a great deal of spin from having been hit far off center. If you didn't notice that spin, I'd say the ball accidentally fell off the tee.

There was no significant wind and I got a good look at the ball--there was nothing awkward about it. He just swung his foot and missed, mostly. This was really hard to not blow dead while things were happening.

We never discussed it after the game--this one had two ejections for fighting and a handful of parents on the field as the second quarter expired. The game was practically a clinic for broken plays and screwy situations. But tempers were still heated at this point and nobody challenged the call.
After checking it out, 6-2-7a applies based on the foul for illegal kick happening before the change of possession. I'd never dealt with a free-kick play foul happening before possession, except for the free-kick out-of-bounds.

This was 4-man in Vegas. WH is on Visitor side about 5 yards deeper than the deepest R player. HL is on the R free-kick line at Visitor sideline. U is on Home sideline 20-30 yards deep, depending on R's formation. LJ is on Visitor sideline at K's free kick line. Just a different lineup, I guess.

Always determine the type of play when trying to enforce a foul.
This was a loose ball play. Enforcement from the previous spot. Replay the down or in this case the kick if accepted.
In most cases, B or R cannot accept a foul on A or K before possession changes and get the ball too.

No qualification needed: free kicks also take place during a down (2-7-1). "Replay the down" is perfectly correct and covers the case.