Omega Flowey is when Flowey absorbs the 6 human souls and becomes a horrifying beast.
Omega Flowey`s battle is the same in "UNDERTALE" but at the end, you are given a choice to hand your soul over to him or not. If you do not give your soul to him, the souls will revolt against him and turn him back to a ordinary flower. If you hand your soul over, he`ll become "Nightmare Flowey" in which he thanks you for being kind and nice enough to give him your soul. The he will take over the entire underground and prevent them from leaving, as the barrier is shattered. He then grows a fond for food, which is why he`ll become "King God of Everything". Alphys then regrets creating Flowey in the first place, but she still is the Royal Scientist
Omega Flowey took everything over, however, you are dead, and your soul is a black soul, a non-existent soul. You gave him the chance to become a god. This will permanently change the game. You will still seem to have the Red Soul, but when you first see Egro, he says, "Did he take your soul too? I knew he was evil.". It then skips their fight completely, showing the credits for the genocide route.
This also affects the Genocide route. Before the Flame fight, she states she's too lazy to fight, and Flowey interrupts, and you fight him instead.