In this instance, it's not necessary to have the word "vous" in that sentence. "Je vais prendre un flétan, svp." is perfectly fine. Although in certain cases, "Je prendrai" sounds better to me than "Je vais prendre". It's the same as if you were ordering in English, you could say to your waiter "I'm going to have a hamburger". That's totally grammatically correct. But for some reason, it sounds better to just say "I'll have a hamburger". It's more direct that way. I think in this case, the maker of the video just added the formal word "vous" to make the request more polite altogether. But try not to let it confuse you, because "Je vais vous...." can be used to mean like "I'll get you...". For example: "Je vais vous prendre un sandwich" could mean, "I'll get/grab you a sandwich". i'd say, just don't get hung up on this grammatical oddity. I'm sure you'd understand it just fine whether or not 'vous' was used in that phrase, considering all the connotation you had :)