You don't need a pressure regulator, the green bottles have the same pressure as the larger tank. I run my Coleman exactly like you have set up. I have to tighten up the connection between the hose and the stove to get the valve open and gas flowing, not just hand tight, need to use pliers.
I also use the same setup. Works great. The only other suggestion might be to check the safety valve on the 10 lbs tank. If flow was started too quickly, it may have operated. Try shutting all down and starting again with slower initial flow?
I use the same setup, works fine. No additional regulator is needed - that silver cylindrical piece that the black hose from the tank screws into is the regulator. It is possible that you have a bad regulator - try replacing.
I happened to be looking at a Coleman hose/adapter myself, on Amazon today. There is a review by "Glassman" which addresses low flow due to a safety in modern propane bottles - and how to re-set it. (Followed by 3 glowing "thank you" comments.) Go to the listing on Amazon, and skim the reviews until you get to Glassman's. Presently, there are five reviews above Glassman's, in the "Most helpful reviews."
I used to have one extension hose that was flaky. Only worked on some appliances, I could run a lantern or space heater but not the stove. Careful comparison to another hose revealed a slightly shorter stem on the adapter. Changing out the rubber gasket for a thinner one compensated and now it works fine.
Did you purge the tank after purchase and have it filled with propane?. Most of the time the "new" 5Lb and 10Lb tanks are purchased from retailers that can not store full tanks inside. They also don't tell you the tanks are full of compressed air.
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