I've not done it with a Brompton, but have with recumbents, so have some idea of the issues involved:
Firstly, you're going to have to adapt the trainer for the small wheel size. This usually means special brackets, which are unobtanium for 20" and I suspect non-existent for 16", so you'll have to do something hackish like this to move the resistance unit close enough to the tyre:
(That's just a couple of pieces of MDF I had lying around with appropriate drilling and bolts)
Then, because the rear wheel is now significantly above ground level, you're going to need something to prop the front up with so the bike is level, and possibly a step to allow the rider to mount safely.
Then you're probably going to want to do the suspension lock-out bodge (jubilee clip, is it? I'm not a Brompton expert) to keep it from sproinging around more than absolutely necessary.
Oh, how trainer-friendly are the axles on a brompton going to be? They're usually designed to clamp around an appropriately tapered internal-cam QR skewer, which may be an issue with solid axles...
I suspect an exercise bike would be much less faff if you could find one going cheap locally (freecycle?).