The Brotherhood anime is quite entertaining (if you are into anime), but isn't really needed, no.
The movie Kingsglaive however, even if it is widely considered to be pretty awful, is needed to understand the world, lore and some important characters, that don't get much or any screen time in the actual game. Kingsglaive is basically the cut out fancy CG opening/prologue of FFXV. Why did they cut it out? To make money or because it is waaaay too long as the opening? Probably both.
But even with Kingsglaive you'll run into a lot of plotholes. That's how FFXV is. Its storytelling is very flawed and incomplete. Episode Prompto and Ignis explain some of the missing stuff, but you should play those after the game or you will heavily spoiler yourself.