The counterspell deck seems too strong... 7 counters in a row in the last game. Each one pumping a creature. How can you win if you can't play anything?!
Since I've been playing this deck way too long, I feel equipped to fill you in. The answer is... you don't.
Just kidding of course. UG Flash will prey on control deck and those slow midrangey things that only look to cast one spell per turn. Make sure you're not its prey and give yourself some stuff to interact with it.
It hates quite a few things - one thing is when you poke at its hand with duress or thought erasure. Once you get a peek you'll see the counterspells aren't nearly as infinite as you thought.
Another thing it doesn't love is instant speed stuff. You will have noticed the general play pattern by now - they only tap out at the end of your turn if you do nothing. If you are able to break that pattern (say by casting something at the end of their turn),
it puts them in a somewhat uncomfortable posiiton.
The obviously love all the stuff that reads "cannot be countered." Explicitly or Implicitly. Field of the dead is out of the picture, but we still have Blast Zone to clean up at least the annoying 1-2 drops.
Similarly, it's really difficult for this deck to stop the cat/oven combo once it gets going. They need to jump through hoops like bouncing the oven, then leaving a counter for a 1 mana artifact if they want it gone. In the meantime, the cat can block
Brineborn Cutthroat all day, no matter how hard he clutches his spiky member with obvious intention, he's not getting through (by the way, the good versions of the deck tend to use Wildborn Preserver instead).
Hydroid Krasis still brings the cards and life and the uncounterable Chandra can clean the board rather nicely; finally, Shifting Ceratops was basically designed as a big fuck you to the entire strategy.
Something like Knight of the Ebon Legion is supper annoying to deal with. Anything with deathtouch will also be problematic because it'll trade with all their heavy hitters.
They also love it when you play shit like Dreadhorde butcher or Tenth District Legionare.
As you examine the deck further, you will notice a few more things:
The mana base is very delicate. They need to get UUGG consistently, but don't want to tap out too much because it means they're not having counterspelling privileges on the critical turn 2 and 3.
If they bumble with the mana, that's your opening.
The only scary stuff they have is Nightpack Ambusher (that motherfucker can take over the entire board in just a few turns), there's Wildborn Preserver / Cutthroat (some lists have an even split of those)
which thankfully give you some time before they take off, and then there's Brazen Borrower and Lizard Wizard with 3 power, but not as spectacular toughness.
The deck can race, but it probably won't outrace a Rotting Regisaur or a cavalcade that's both on the play and getting all the gas.
If you're trying to beat it at a longer game, Spectral Sailor is its only source of card draw, and some cuntnuggest have the bright idea of only running three of those. Bottom line is, they'll run out of counters eventually,
and only have precious few ways to reload. The problem is you gotta stay alive until that point.
The big question is obviously how to resolve spells with a deck that doesn't want you to. This applies especially for something like Teferi, which swings the game heavily in your favor (but remember, it's not dead yet, it's difficult, but I won a handful of games after a resolved teferi).
Obviously, you don't play into counterspells. if there's nothing to gain. If you see an untapped 1UU, doesn't take a genius to figure out the end result of that play. So, play your shit fully expecting them to have the counter on hand, because that's what the deck does.
You can start making gambles that they might not have a counter once they're down to 1-2 cards in hand, but until they're spent like so, the only game you may have is counterspell baiting.
This is where your 1-2 mana cards work best.
EDIT:
If you're looking for specific tips for this matchup with Dance of the Manse, let me tell you straight off the bat that you're not really the favored side here in Bo1. Your most important spells would be Murderous Rider, Teferi and Thought Erasure and I would recommend upping the count on those to 4x if you're seeing a lot of Flash. You can try adding a few extra things like Despark (mostly to answer Ambusher), Disfigure can also kill their lesser creatures, but is an excellent end of turn bait to force a wrath or teferi through. In Bo3, I would consider bringing your own Mystical Disputes and Duress.