I'd recommend trying using a heat gun. It won't be a perfect method, but it might work. The only problem is you still might have to use a chemical treatment afterwards, but it'd be much less. If the brick surface is very rough, sandblasting might be easier.
Here's my advice.
Get a canvas dropcloth to protect the floor from hot paint.
Purchase a heat gun for about 20-50 bucks from HD or one of the other ones.
Test the application of heat on an area that can be hidden. Apply the heat until the paint bubbles.
Use a piece of plywood for a paint scraper.
Be very careful, have a buck of water nearby, expect the scraper to get hot, wear leather work glvoes, safety glasses and a long shirt and pants, hot paint chips aren't fun. Make sure the area is well vented with windows open, etc.
Once you've lifted all the paint off with heat, finish the cleanup with Dayco Marine Stripper. It is nasty bad caustic and evil stuff, but it works pretty good.
It's a lot of trouble and will take several long days or even a couple weeks, good luck, and mostly, be careful, both for yourself, and for the room you are doing the work in...