You can paint it but the brick pattern will still show. Would look a little off closeup.
Yes you can. We had that professionally done to our concrete patio & pool deck. But it didn't look all that difficult. They used a 1/2 inch wide double sided foam tape that was about 1/8 inch thick (Scotch makes it). Use the tape to mark out your "grout lines" between the "flagstones". Then they spread a thick reddish (choose your color) coating over the whole thing. After it dried well, you go back and peel off all the foam tape revealing your grout lines and you have a very realistic flagstone patio! Removing the tape was very tedious, but it looks great. I would think, that over a brick patio, you might want to coat the patio with a thin concrete slurry first to hide the brick that would show through in the "grout lines" or spaces between the faux flagstone.
Read my answer again. I did mention that, because of her brick patio, she might want to coat the bricks with a thin layer of concrete to hide the brick. I think it would look fine.