All right as neophyte machinist I remember several years ago that Mark Stratton had an article on his web page about how he milled an octagon barrel. I wish I still had it but I was wondering if you could do a tapered octagon on a manual milling machine?

Sure,
There are 100 year old rifles around with tapered octagons.
The first rifle I ever fired was a 12C Remington pump with a tapered octagon barrel. That gun was a worn out clunker then and that was more than 50 years ago.

you'd have to hang the barrel off the edge of the table (chamber end) and build a fixture to level the barrel to the tool and taper you want. A 5c collet indexer to rotate the barrel 45 degrees.
Do it in two passes as there is not enough travel in the X axis to machine it in one pass.
Sure it can be done.

Just remember:

SUPPORT the back side of the barrel when cutting, otherwise the work will deflect differently as each flat is milled away, causing a corkscrew bore effect.

If the mill-scale skin is still on the barrel then either turn it off before milling or else mill the flats in opposing pairs, 180 degrees opposite each other with as little delay as possible between cuts, to avoid having the as-yet-uncut portions of the skin warp the barrel.

I'm merely a shade-tree machinist, a REAL toolmaker can give you lots more tips.
Regards, Joe

Support is absolutely key. Worse then a cork screw bore is the fact that the milled finish will look like crap and if not supported enough it could fly off the table and damage you, the machine and the barrel.
You should really think about building a fixture for this.
And it should be machined on the slow side with lots of coolant. As JD said cut it on opposite sides. Mill scale or not a heat treated piece of steal is going to warp if not machined correctly. You should take equal amounts off of each side and no more then .030 to .050 per pass i would take less then that rotate the barrel 180 and and take the same from the opposite side going back and forth till the proper amount has been removed.
You could clamp it to the table cut one section then move the clamps and cut the other section. It's a pain to do it as a one off part. But you will need to draw file it anyway as a milled finnish won't look good anyway.
Chromolly is a little more forgiving but stainless would be a royal pain. Just take your time with it.