John, thanks for asking.
There are two good questions in your post. Here is how I interpreted them:
Can I use aluminum flex to wander through my tight up and over situation?
The ICC building code does not allow the use the aluminum semi-rigid flex in any concealed spaces (walls, floor joists, attic or crawlspace). For your situation, although likely convenient, the material thickness of the flex would further reduce the opening as you squish the hose, lessening the efficiency. If you ever sold your home and the buyer’s inspector was observant, he may require that the semi-rigid pipe get replaced with hard pipe (rigid). So, the rigid pipe is more efficient, safer and per code, but a bitch likely for you to make the configuration you need.
Can the exhaust conduit touch the combustibles?
The code does not mention or require that the pipe maintain any separation from the wood studs, beams or drywall. Generally the temperature does not get over 155 degrees in any of the pipe surfaces. Taping the joints with the silver tape is a good practice to better contain any fire within the conduit.