I cook flats all the time, and lots of people completely trim the fat cap when cooking packers. The moisture in a brisket doesn't come from the surface fat, it comes from the breaking down of the connective tissues between the muscle fibers.
Below is a pic of a slice of undercooked brisket:
See the little squiggly lines the arrows are pointing to between the muscle fibers ? That's connective tissue that hasn't broken down and rendered yet. This slice of brisket would have been somewhat dry and elastic.
A nicely cooked brisket
In this one, the arrows point to where you can see the muscle fibers separating. The connective tissues have been broken down and rendered into liquid. This slice would be moist and tender. It would come apart with just the slightest pull.
It's a somewhat narrow window that you have to hit. Generally speaking, pull the brisket too early and it will be dry and somewhat tough. Cook the brisket too long, and it will be dry and crumbly. To make things even more difficult, the size (or duration) of the window will vary depending on your chamber temp. The lower the chamber temp, the wider the window.
These are some of the reasons why brisket is the second hardest thing to smoke correctly (first is whole hog imo). The way to tell when a brisket is done is to do the poke test. Poke the brisket with a probe along the thickest part of the flat and when the probe goes in and out with no resistance, the brisket is done. That said, even this takes somewhat of an experienced hand as "in and out with no resistance" is up to personal interpretation to some degree.