I'm no industrial chemist, but from a glance at the chemical formula [1], I'm going to guess that it could be produced by the trainload (provided that you shoot the FDA first, which we should have done on the first day of the epidemic judging by their track record so far)

[1] https://en.wikipedia.org/wiki/Hydroxychloroquine

Former process chemist here. Yep, you could produce trainloads of this stuff within the month if you bypass the FDA, and even if you do play by the book, current capacity could easily crank out kilos of GMP HQ a day.

Could you expand a bit on the required base materials and possible bottlenecks? Would third world countries be able to produce this, and would export restrictions on reagents/chemicals limit production for some countries?

There were 5.7 million american prescriptions for Hydroxychloroquine in 2017, and the wholesale price quoted on wikipedia is 5 dollars for a months worth of pills.

I don't know how difficult scaling up production is, but the above numbers make me hopeful.