I had to do some re-work to the chimney in my house, what was existing wasn't close to code. You can access NFPA 211 online, and that has all the proper clearances needed for the pipe you want to use. NFPA is THE standard for any/all things related to fire protection. The verbiage they use can be a little tough to understand, but doable.
I think I would run through (not threw) a wall and up instead of two breachings (floor and roof).
I searching on line it becomes clear many places make completely false statements about what you "have to use", in order to sell products. Trust NFPA.
