This comes up fairly often. Usually it is caused by the excess flow device located in the gas line by the regulator. The device is designed to prevent rapid escape of gas in the even a line is cut. It is a spring loaded piston with a small hole through it. When you first open the valve on you tank, there is no pressure in the lines downstream so the gas can flow very quickly, which triggers the safety device. By cracking the valves on your tanks open very slowly you can prevent the safety device from triggering.
Usually after a few minutes the pressure will equalize on each side of the safety device, provided you aren't using any gas for those few minutes, and the device will automatically reset and then you are good to go. However, if you try using any gas or if you have a leak in your system the device will not reset and you will get a very limited flow of gas.
2011 Skylark 21FKV