Reddit mentions of Chimney 24636 Flash Seal Sealant, 1 Gallon Capacity, Black

For the chimney, what the hell is the inspector talking about when he says the chase need "prep and recoat"? I've never heard anyone in this profession say anything like that, unless he's talking about the crown. If that's the case, you could apply Crown Coat to it, the company technically doesn't sell their products to the general public because they'll always recommend a professional to do the work, but it looks like somebody is selling it on Amazon. It's pretty easy to apply, just pretty much paint a couple coats of it over the top of the crown, and it's cured in about 2-4 hours, plus there's directions on the bucket.

For the flashing, I also recommend another one of ChimneySaver's products, Flash Seal. It's another fantastic product and works great. Just put that flashing back against the roof and apply the seal as directed.

The relining of the flue is something I will absolutely insist you hire a professional to do, you are literally playing with fire here, not to mention inside your home. Contact a reputable CSIA certified chimney sweep to get an estimate on getting that properly relined. I don't know what the companies in your area do for relining, as there are several ways to do it. My company only does it one way since it's the only method that has been proven to us to be completely reliable without breaking up quickly or being an overall shitty job, and that is with a stainless steel liner, so try to find a good company that will do that.

For the rain cap, there are also several approaches to do that. If you get the stainless steel liner like I recommend, they will probably have to break out your old damper to access inside your smoke chamber to parge it and seal around the bottom of your new liner, so what they should do there is apply a top-mount damper, which basically works like this, so it kills 2 birds with one stone, plus the flue is sealed air-tight when it's not in use with these, as it has a silicone gasket seal. If not the damper, you could either get a cap that covers that lone flue, or else one that will cover the whole chimney chase, depending on if you have more flues on that chimney or not, and your personal taste. I will recommend getting stainless steel ones no matter what though.

That should be everything for the chimney, unless you REALLY trust these sellers, I'd recommend getting credited for the work, as they'll probably have someone half-ass it for as cheaply as possible, and that's one thing you do NOT want to half-ass.