" Can I insist that a contractor use unseen parts of the rear roof as salvage to replace any shingles damaged in the chimney repair, or is that impractical? "

Completely impartical and your risk leaks in other places by this attempt. Around a chimeny why do you think it is a shingle issue? I would look at the brick, and the flashing around the chimney . Unless of course you are speaking of shingle areas "near" the chimney. If there is no match for the shingles, how old is the roof? Realistically get the closest you can find and it will stick out, not much else you can do without changing the roof shingle. What about changing only this elevation for now?

When I replaced a roof, I was amazed by the options. Take a bit of your existing roof shingle and go to a store that sells roofing and compare to all of their samples.

"Can I insist that a contractor use unseen parts of the rear roof as salvage to replace any shingles damaged in the chimney repair, or is that impractical?"

That would depend upon the age and condition of your shingles. A roofer is going to charge a very heavy premium for this, believe me.

millworkman is on the right track. It may not be the shingles leaking.