If you can get some big box section 100 150mm that will do it,we scrap loads of that so a root around in a good scrappy may be productive, old co2 bottles welded together sound a good idea as does lamp post, old flexible central heating flu liner can be used on top of a solid flu to get the fumes away, but the initial part of the flu must be quite thick, I am considering using an old soil pipe/land drain (pot) but dont know if it will stand the heat, you need some thing quite thick, these things get hot!
Actually it depends what you want is for, if its just a chimera type garden heater ,then, after its lit and the initial smoke had died down these things burn with a fierce clean heat, a bit like a barbie,with not much smoke at all and if you make one out of a tall bottle its already more of a chimney, a short mild steel stack pop riveted together and stuck on top (assuming you can roll it first) will do.
Anyway ,dont want to sound like an expert,i,m not ,just bodging along like you.
I fancy making a horizontal one out of a tall bottle with a flat surface for cooking on,guys are making pizza ovens ,also you should google rocket stoves ,these are really efficient at home heating. A lot of people struggle to get the valve off, our gas supplier does this all day with a special tool and jig and did mine for nowt,always worth asking.I have since made my own spanner .The gas does linger when the valve is off , so always fill with water after.
The initial burn will kill the smell and melt the paint enough to scrape it then you can spray them up nice ,the paints not cheap tho.
cheers Spud.