Jeff,

Technically it's a vent, not chimney. The flue is the space inside a flue liner. I don't recommend painting. Vents can rust from the inside out so paint won't do much. Eventually replacement will be necessary but for now it's ok.

As for the shingles. It's more a question of flashing, as in, where is it?

__________________
Eric Barker
Moraine Woods Consulting, Inc.
Barrington, IL