OK, I'm not an oat expert, but I would suggest that when buying grocery store oats, have a look at the cooking directions, and use that as a guide for brewing. Checking out Quaker's website:
* Steel cut oats - cook 25-30 minutes
* Old fashioned oats - cook 5 minutes
* Quick 1 minute oats - cook 1 minute (or microwave 1-1/2 to 2 minutes)
* Instant oats - No cooking listed, just microwave 60 - 75 seconds
Again, not an expert, but I'd suggest that instant oats will more readily give up their goods in a mash than any others, with 1 minute being the next best, old fashioned in 3rd place and obviously steel cut last. I'm certainly not ready to think that old fashioned, quick and instant are interchangeable.
But... perhaps after a 60 minute mash, maybe they indeed are the same? There's probably a y=mx+b thing going on, where the longer you go or the higher the temp the more you get out, perhaps all of them getting there after an hour at mash, making them interchangeable after all? Or, maybe there's a minimum threshold and something closer to boiling temps is actually required?
As far as flaked oats from the LHBS I couldn't say.
Someone should buy all the oats, mash a pound of each (separately of course), measure the gravity of each afterwards and let us know