I would try to find another tank to just test it with rather than buying a new tank. But, you can take it to a walmart or other similar store and do the tank swap, where they swap one tank for another filled one.
another thing to check is the condition of the burners. If they are all corroded or gunked up and have restricted or plugged holes, you will get much lower performance. But, with the flickering that you describe, it sound more like a propane delivery problem.
Also, have you checked to see if it is just one or two burners that are burning low or is it all three?