My understanding is that there is no simple (or even a complex)
formula, just some generic guidance.  In classical organs this type of
pipe is known as Rohrflöte [Chimney Flute] and the chimney dimensions
vary greatly.

The internal dimension of the chimney tube can be 1/6 to 1/3 the body
diameter.  The length of the chimney can be 1/4 to 1/2 of the speaking
length of the pipe.  The dimensions that any particular organ/pipe
maker settles on are most likely based more on the desired tonality of
the stop and the artistic results of voicing work.

What would be an ideal answer to the question would be measured
drawings of a specific set of pipes that you admire the sound of, but
I don't know who might be able to do that.

Brian Shaw