Kelly, I would hope that one of the plumbing and heating pro's check in on this. But to help us answer this, does your chimney have clay liner blocks and what condition are they in? That's the real question about your chimney's health. I know that, with this cold winter, we are having more condensation of flue gasses inside the chimney this year. The condensate is very acidic and will eat the mortar out between the tiles and sometimes the mortar between the blocks. This could be the real problem you may be seeing that's causing the question.
A stainless steel flue pipe installation is a job for the pro's because of the special mortar, mixing, and installation requirements.