Since Victarion definitely wants to prove his loyalty to Dany, I think there could be several explanations as to how he made dragon banners, and a lot of people have already offered some good possibilities.
p339 ADWD part 2
"The sorcerer priest was garbed in black, but for a hint of golden thread at collar, cuffs, and hem. There was no red cloth aboard the iron victory, but it was not meet that Moqorro go about in the salt-stained rags he had been wearing then the Vole fished him from the sea, so Victarion had commanded Tom Tidewood to sew new robes for him from whatever was at hand, and had even donated some of his own tunics for the purpose."
While it says they made Moqorro black and gold robes because they didn't have any new red fabric, it does reference Moqorro's salt-stained rags he had been wearing when found. These rags were red, and even if they were not salvageable as clothing, they might have yielded enough fabric to produce some red dragons to sew on the black banners.
Other ships in the fleet, other ships he might've 'claimed' on the way to Slaver's Bay, maybe he had some dye. I don't think it's too big a deal, really.
This sounds pretty plausible. They did gain quite a few ships along the way that could have had red fabric or dye.
I'd prefer if it were Vic myself since Euron showing up is silly. But, the paragraph just seems to lay a lot of stress on the absence of red either for clothing or for banners. A later chapter having the whole Iron Fleet raise dragon banners seems odd. Especially since Vic was meant to be on the cusp of entering Mereens bay when ADWD ends. He doesn't mention such things beforehand.
I think this may be one of those details that George RR Martin won't take the time to fully explain and will hope we just come to our own conclusions like some of the ones brought up. I know we like to put a lot of thoughts into the books during our long wait.
On Euron, while I don't think he is the one who has raised the dragon banners outside of Meereen, I have always thought he somehow found a way to tag along on Vic's mission. I can't see him sending Vic off to woo Dany and have the opportunity to steal what Euron wants for himself. I also think that Euron is the true master of the dragon horn. Moqorro says the dragons will only come to the master who has claimed the horn with fire and blood, and I can't think of any way Vic could have done that. When the horn is blown, if the dragons respond to any master, I think it will be Euron and that is my main reasoning on why he is there. If Moqorro wouldn't have landed with Vic, he would have blown the horn himself and died so why wouldn't Euron be in the wings waiting to swoop in and claim the dragons once his brother is dead for blowing the horn.
Sorry to get off topic, OP!