Gas burner is “clicking” – how can I stop this

Where do you live? European Pyrex is made from borosilicate glass, the same as in laboratory's equipment; American Pyrex is made from common soda-lime glass.

If you are in America, don't bother trying it at all; soda-lime glass is sensitive to thermal shock. Even though it's tempered for kitchenware, it is nowhere near good enough for the burner.
In Europe, you could take your chances if you have a bowl you don't mind risking. However, there is still a significant chance that it will break on the burner some day. While I think that they use the same raw material for both kitchen dishes and laboratory test tubes (which are obviously OK on a gas burner), kitchen stuff is much thicker. This makes it much more likely to break under thermal expansion.

If you decide to make the experiment with a borosilicate Pyrex, take care to warm it gradually, starting with a small flame, and don't pour cold ingredients into it. Proceed at your own risk. And ask yourself if you really have no pots better suited for the task.

I've got a 6 burner cooktop with a 16k, 3 12k BTU burners, and two smaller burners. My standard household gas line can supply at least 5 of the 6 concurrently without problem (haven't had occasion to use all 6 at once yet). The gas line feeding it is the same size as the rest of the gas lines in my house. Also, according to the installation instructions, the input gas line must be the same diameter or larger than inlet line of the appliance.

Inferring from that, I'd say it is going to be dependent on the inlet size of the stove you select. I don't believe line pressure will be a problem.