3/8 " is the lowest I would go for flat paint.

Why? What if it was eggshell or satin?

Well, if you are looking for very low stipple I would try 1/4" for eggshell. With flat I would be concerned about being able to get an even finish with 1/4" which is why I would go with the 3/8". Normally with flat I use a 3/4" nap and with eggshell 1/2".

Thank you for answering. I’m trying to understand the difference. I guess paint with a sheen covers better than flat? This BM Natura Flat does have a slight sheen to it and it is very thick paint. The painter I had to fire had trouble spraying it, but he had only used SW paint and apparently was not experienced. What’s your opinion of spraying paint and back rolling? And, when you roll, do you roll in one direction and not overlap?

Spraying paint and back rolling is probably the best way to apply the paint evenly. If you are rolling manually out of a bucket or whatever, the time it takes to load the roller with paint is what makes it hard to keep a wet edge, especially if the walls are big. If you can't keep a wet edge, this is how lap lines may show up. If the Natura is washable, it should be just as easy as applying an eggshell. True flat paint doesn't form a washable skin on top of the paint film when it is dry and is filled with cheap fillers like chalk so that is why we use the bigger naps for flats. The best way to roll either paints though is to apply it, and then make your final pass with the roller in one direction top to bottom.