You don't want to buy Floodgate after you play Auction. You want to buy Floodgate while Auction is still in your hand so that the Floodgate, Auction, and any other dead cards in your hand all carry over to your next turn. Get +$1 for that Floodgate!
that's true, but that's something you can do regardless, it doesn't change the anti-synergy if you have auction in your hand and want to buy a floodgate. it's minor though, no doubt. if making a simple card even simpler is worth something to you, you probably want to keep it as it is.
I see Auction and Floodgate as having a very strong synergy, even if they're both slightly inflexible to use. I've played one game with Floodgate, but just about every time I had a spare $4, I had nothing else in my hand worth setting aside. It'd be nice to have a card that benefits from increased handsize, which might even tempt you to set aside Floodgates with Estates and Curses. There's plenty of room for more Secret Chamber variants, and this is original and mechanically clever.
Floodgate's a good card, but it needs to cost $3; I said this already, but in order for the combo to work, you need to plausibly be able to buy Floodgates without playing your Auction. From that perspective -- because that change looks more necessary -- buffing Auction and Floodgate simultaneously would be a bit much.
