Let me just start by saying that I'm new here and the only experience with composites I've had is some simple fiberglass lay up by hand. 

I want to make a rectangular carbon fiber tube. I've done some preliminary research here but failed to find a thread about this specific type of project. I was, however, able to determine that I probably want to use the vacuum-bagging method.

I very much doubt that the tube in the picture is "seamless" -- You can not weave "Twill" in a continous "tube" ---

If you want a cosmetic outside part like the one in the picture, AND you want 2-2 Twill, then you will have a seam ..

If you use braided tube, you will have the braided finish, that looks like plain-weave - only without 90- degree  angle to the weave .. it will usually be a steeper angle.

Also Braided hose CF is quite "open" in the weave, so the lower layers need to be a black material. (Not Glass-fibre)

I would make a split mould, and vac-bag with a pressurized rubber tube through the inside, to get a good cosmetic surface.. I.e. make a "plug", then make a mould from that.

Another option is to vac bag on a mandrel (slightly tapered) and use very carefully applied Peel-ply on the outside.. It can then be clear coated to give a good cosmetic finish.

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