So here is the set-up:

A single-speed free wheel (22 cog) in the back with a 1/8' SRAM PC-1 chain. A single speed chain ring in the front. When down hill or in the flats, it appears to be fine, but when up hill or sprinting, it skips, but when it skips, the Surly Singulator (which is set for the downward or outward) facing spring, actually gets pinched in (i.e -get moved up, and closer to the chainstay until it releases).

What is the cause of this: I assume not the rear freewheel (22 COG SS free wheel) or the chain, both built around the 1/8" chain. Is it the front chainring?

The times I've experienced skipping chain, it was either a worn out chain, worn out cog, or both. Skipping after a new chain seems like a sure sign of a worn out cog.

This can happen if your chain line if off.

What is your frame?

I experiences this myself been pulling hair off frustrated why my old beater bike got skipping everytime I accelerated hard on red light. Its not single speed, its normal beater bike with gears. I looks at the chain, its good, cog also good, chainring good. I scratched my head so hard why this annoying phenomenal happens. Got LBS to check the bike for me because I really have no idea.

They ask me to show them what happens, I did the same and chain skipping. They told me you accelerating way too hard for your "frame". Your frame is flexing hard.

Its bike frame that cause this, its cheap no butting hi-ten frame I use for beater bike. Now, I carefully accelerating, no hard mashing or chain skipping happens.

Is the derailleur hanger aligned? Has it ever been checked? If it were out of line, the jockey wheel would be sitting askew relative to the chain. (Just speculation but the issues with derailleurs and mis-aligned hangers is well known.)

Any shop can place a tool on the hanger, check alignment and true if needed. (You can too but the real tools are expensive. Making your own good one isn't too hard.)

So for my situation:
(a) Brand new Sunlite 22 cog rear free wheel (for single speed application).
(b) Brand new SRAM PC-1 SS/FG chain.
(c) From chain ring seems okay, but it is old. Going to replace that to see if it help.
(d) The chain line appears to be correct and aligned.

Bike: Raleigh Technium 460 (50cm) - Aluminum main frame, with rear triangle comprised of steel seat & chain stays.

The Singulator is set to exert downward facing tension on the chain, and when climbing even mild grades or exerting moderate force on the crank the chain appears to tighten up, and pushing the Singulator up towards the chain stay, until the pressure then is relieved somehow, and the Singulator snaps back into position.

Curious why, if the chain were slipping, it would cause this tension to push the Singulator up.

If the chain is slipping, it means it's temporarily riding along a larger diameter arc around either the cog (more likely) or the chainring. It's like switching to a bigger cog on a derailleur bike -- something has to compensate for the increase in arc length.

How long is the chain? I'd guess there should be a rule for chain length similar to the rule for a derailleur bike, except that big-big is just the gears that you've got.

If you've checked and know your ring, chain, and cog are good - then it should logically follow that as it is your chain tensioner that is misbehaving, that it is the tensioner itself that is the culprit.

They are not that expensive - perhaps you should try a different one.

Good luck...

Thanks everyone for the guidance. Once the front chain ring is replaced (at this point, the most likely culprit I hope), I will re-check the drivetrain and hopefully this will be fixed.