Scrimmage Kick, kicked out of K's end zone
 

4th and 10 from K's 15 YL. Ball is snapped over K1's head and into End Zone. K1 chases ball into end zone and kicks the ball across endline. Safety...yes What is the proper sequence of events (bean bag, flag), options, and Rule Reference.

Thanks

Flag the spot of the kick. Ball is dead when it crosses the endline, give safety signal.

Penalty accepted - enforced from own end zone - safety. 10-5-4
Penalty declined - ball dead in K's own end zone not in player possession and K responsible for forcing it there - safety. 8-5-2b

Why flag the spot of the kick? What's the foul?

From the OP, it reads as if the "kicker" never recovered the bad snap and kicked the ball while it was loose ... Illegal Kick, Spot Foul

Illegal kicking... he didn't specify that he picked it back up and punted it, so I assume illegal kick.

He did not pick up the ball....simply kicked while it was rolling on ground in end zone.

I see. That's illegal.

So you asked about mechanics. Here are some:

1. Flag the spot of the foul (endzone).
2. Signal safety as the result of the play.
3. Offer choice to R:

a. take the result of the play, a safety

b. take the penalty, a safety (not much of a choice)

4. Have K free kick from their 20.

As it happens, since the foul was in the EZ then the result is the same whether the penalty is accepted or not - Safety.
But you flag it anyway as it looks odd not to flag it. I train my guys to keep it simple and follow their routine. In this case - see the foul, take a second and replay it in your head, decide "Yes thats a foul", flag it and keep officiating. Don't over-analyse and start thinking about the enforcement while you are still officiating.
I use the same philosophy for bagging fumbles - bag them all and keep officiating, worry about whether you actually need that spot later on.

What if the foul had been on the 1 yd line? I have seen officials over here in the UK (where we play NCAA rules and illegal kicking also caries a loss of down) who don't flag it, just go with the safety and only later do they realise that maybe B would prefer to forgo the safety, take the penalty and get a 1st and goal.

Yes a safety no matter what:

NF - not wanting to change the subject, a minor detail, but technically there is no need to bean bag a fumble behind the nuetral zone. If a penalty occurs the basic spot is the previous spot as the fumble or kick or snap is a loose ball play...

Indeed. I get over to the US periodically in the Fall and when I do I make sure I bring my kit and work some HS games, so I have to know Fed Rules too.

But even then, my philosophy is "see a fumble, bag it". Don't worry about where it is in relation to the NZ. There are more pertinent things to think about while the ball is loose from the fumble and you maybe can't afford to switch off for even a 1/2 second.

Bag it, keep officiating. You can pick it up later if it isn't needed.