I would like to paint the threshold in a black matte finish.
The key to a good paint job is going to be prepping the floor thoroughly! I would also recommend priming to get the best adhesion. Also because it will receive so much wear, it is important to seal with a strong top coat. Here is some more info! https://www.bobvila.com/articles/painting-tile-floors/
Hello. I have personally not done this project —but here’s a link that might be helpful.
I see that you've received help for painting your floor. I just wanted to let you know that you might want to rethink your matte black. The reason is that it will show every single piece of dirt, dust, animal fur (if you have pets) and it's very hard to keep clean. I'd suggest that you paint an extra tile matte black and put it near your door to test how it will look in use. Make sure that people step on it like they would a threshold. Once you've seen how it will react, then make a decision. Wishing you the best.
Take a good photo of the area or a section of the tile to the paint department of your home improvement store and ask them for advice on materials, application tools and techniques to do a successful project.