I love making hats, and though I've never tried making my own felt hat (I have given a few felt hats snap brims however), I've been researching how to do it for a little while. Essentially what you need to do is to buy a hat blank (I think blockade runner has some wool-felt ones for sale), and a hat-block, this could be a proper wooden one, or it could be a custom-made foam one. There are tutorials on YouTube on how to make a foam hat block, if you wish to go with that option.
To make the hat, start by heating up a kettle (or steam mop, clothes steamer, steam iron, etc.) heavily steaming the hat, and stretching it over your hat block. Next, place a towel over the hat and use an iron on a low setting to shape the crown. Then, tie a hatter's knot around the base of the body (where the crown becomes the brim) and use a wood tool, along with your iron to form a crisp "break line" between the crown and the brim. Since you want the "Ol' Rebel Slouch Hat" look, I'd say to refrain from pressing the brim, and if you want, you could even pull up the right side of the brim to get that mishapen slouch hat look that Dewett's hat has. You can further stylize the hat by holding the part you want to form over your source of steam and using your fingers to mold it.