It's possible it's Taim idea all along, but from events in LOC it seems unlikely Demandred didn't have a big hand in it.

Taim expected to be taken as Rand's second at his side, in fact as his equal at his side. He was very clearly pissed off to be sent to the Farm and to have to train men there. At the next meeting his attitude had completely changed - he brought up the notion of recruiting, which was a major factor in the success of the "Shadow army hidden in plain sight" idea. Then Taim got his SG rock for his speeches, and it stretches credibility that overnight just like that he became a specialist of military organization. Ranking system, the layout of the grounds, the discipline, the indoctrinement, the training. That's a whole lot for an amateur. The whole thing reeks of Demandred's involvement at the early stages. It's pretty clear he advised Taim, though I'm sure he didn't take too direct an hand. Another thing to consider is who made Taim so paranoid about Rand's safety... which lead to Dumai's Wells. The book ends with Demandred being extremely pleased with himself too...

None of this undermines Taim's achievements. Demandred wasn't holding his hand. He really did all the field work, convinced Rand to trust him, convinced Rand to allow him to recruit and so on.

The comment about Demandred vs. Flinn is overstated. It merely means Demandred was not familiar with the Asha'man, it doesn't mean he wasn't advising Taim in the building of the BT.

Even before the Cleansing Demandred knew about DF Asha'man and was giving them orders, and warning them not to repeat their previous book's blunders. He was also acting in Taim's back at that point, and Moridin was Nae'blis, had sent Osan'gar to the BT and all. That's why I think Demandred set up the BT, one of a series of ventures to build himself forces to use in TG IMHO and not one of those he's most involved in I suspect as Taim was there for that, but he realized early Taim had divided loyalties. It may have to do with knowing all along that Taim is a DF who has been set up as False Dragon by Ishamael, that Demandred tried to replace Ishamael as his patron after TDR but Moridin's arrival meant he could no longer trust Taim to be fully his anymore. Mesaana was more or less in the same situation with the BA the rest of the Chosen were using as well (and yes, I think she built herself a group of agents in the Tower she had exclusive control over and that she preferred to rely on rather than Alviarin and the BA exclusively).

It seems obvious Demandred must be super pissed Taim was raised as his equal as Chosen. For sure there's gonna be some power struggles between those two. If my suspicions are correct and Demandred is in a "Taim would have achieved nothing without my help" viperous mood, we'll see some of Demandred's displeasure in some of his POV. He's just way too clever to show any of this in front of Moridin. I guess odds are we'll learn quite a bit more about how the BT came about.