How do you keep chips out of all the tapped holes on a fixture plate?

With that many holes, plugs and caps are a losing battle. You'd spend twenty minutes a setup popping them in and out and half of them whould end up under the mill table. What I did on my plate was thread a short socket grub screw into every hole I wasn't using. Cheap bulk pack of M6 or M8 set screws, driven in with a hex key, sitting a hair below flush so they don't interfere with the work. Chips still land on top but they can't get inside the threads, and if a used hole gets fouled I just back the screw out and move the clamp. You only ever keep the handful of holes you actually need open for that job, so the cleanup problem shrinks to two or three holes instead of three hundred.

For the holes that stay open, a tap chaser or just the same tap you cut them with, run through by hand once, clears the packed swarf fast. Takes a few seconds per hole. A stiff brass brush on a drill works too if the bits are just sitting in the bottom and not jammed in hard. One thing that helped me alot was blowing the plate down before I even start the cut, not after. Chips that get in during the cut are inevitable, but the ones that really jam in there are the loose ones sitting around the hole mouth that get shoved down by the workpiece when you bolt a clamp on. Vacuum first, then air, then set the clamps. If your plate is thick enough you coud also consider drilling the next batch of holes through and putting a spoilboard underneath, then you can blow from the back through an open channel and push chips out the bottom. Not worth redoing what you've got, but worth thinking about if you ever make a second plate. And yes, some grit is just part of the deal, but it shouldn't ever stop a bolt seating flush. If it does, the swarf is packed hard enough that it needs the tap treatment before that hole gets used again.

Same expirience here, the set screw trick is the only way a big grid stays usable. One thing I added on mine was a quick chamfer around each hole mouth with a countersink bit. Chips get flung off by the spinning workpiece instead of dropping in, and a bolt passing over the edge seats flush way easier. I also keep an old fridge magnet taped to a stick and touch it to each open hole before threading anything, pulls the fines out of the bottom that air misses.

The grease trick is worth a shot too. I put a light smear on the bolt threads before running them in, the grit sticks to the grease instead of jamming at the bottom of the hole, then wipes off easy. My plate took me two full evenings to tap out something like 250 holes and I got sick of chasing threads, so now I just grease the bolts and only run a tap through the odd hole that gets truly packed. Cut a bolt about half an inch shorter than the plate thickness while you're at it, so nothing bottoms out if a chip does end up down there.

I always check my tap first. If it's galled or stripped, it won't pull the chips out of the hole properly, no matter how careful I am. I just run the tap through a scrap piece of steel to make sure it's biting correctly. I've also found that if I size the hole just a tiny bit larger than the final thread, it gives the swarf a bit more clearance so it doesn't just jam in the bottom.

Mine's aluminum, which changes the picture a bit since the chips come off fluffy and mostly sit loose rather than jamming in hard, so a quick puff down each hole before clamping covers most of it. One thing I noticed after chasing the same hole three times is that the grit that stops a bolt seating flat is almost always in the first couple of threads, not the bottom, so a short two-turn scrub with the tap fixes it. I also keep a china marker on the shelf and circle every hole I've used that session, then clean just those before the next setup.