Each unit comes equipped with 3 bed, 2 bath, attached 2 car garage, quartz countertops, advanced soundproofing, 2x6 exterior construction, premium vinyl siding / Provia stone masonry, 5/8" drywall, separate concrete driveways, LVP Durato flooring, and a fenced-in backyard for pets / family.

Don't paint masonry.

That said, as @Pat L. mentioned, running stand alone flue pipe through a masonry chimney is not uncommon at all, for the very reasons you're asking.Keep in mind though, you'll likely need a custom cap made to keep out the elements and critters.On another note, if the chimney is "flaking all over the place", is it sound?

(Danny Wells Masonry, Redemption Roofing, Wood-n-Deed) We also had to hire a lawyer when Beam refused to refund any of our money or fix their damage.

A small masonry chimney was pulling away from a stucco house.

You might have to dig down and add on to the footings.ETA: Patricia has a good point about contractors not wanting to deal with renovating masonry houses.

It has some faulty wiring and needs a little masonry work. 

By the sound of it, the property will need a porch repair, masonry work, landscaping, and windows.

I would have a couple of local masonry contractors give me a quote for the repair  work.

Call some concrete companies or masonry companies in your area if your trying to put a Band-Aid on it.