Being that this is not a flat tappet cam set up what is the proceedure for this on a new 22re with new head rings?

 

New head rings? I assume you mean new head and new piston rings, correct?

Flat tappet or not, the 22RE does require a specific cam break-in procedure. Which you could have easily found if you'd searched.
https://www.yotatech.com/forums/f116/22re-break-165608/

After the cam break-in, I highly recommend the "run it hard" break-in process for the rings. It's worked perfect for me.
http://www.mototuneusa.com/break_in_secrets.htm

One more thing, break-in oil. As in ZDDP. Add it to the oil, something like STP oil treatment. Or use a high ZDDP oil, something like diesel oil or oil labeled specifically as "break-in oil". And if you didn't already grease the cam lobes and rocker arms prior to initial start up, you might want to consider doing so.