"一手同花大牌" can be translated into English as "a big flush hand" or more specifically in a poker context, "a strong flush hand".
"Flush" refers to a poker hand where all five cards are of the same suit.
"Big" or "strong" emphasizes that it's a high-value or powerful flush hand.
If you want to emphasize that it's a particularly good or winning flush hand, you could also say "a winning flush hand" or "a top flush hand", depending on the context.