how is using dark pulse three times giving you a statistical chance of flinching? Even with 3 dark pulses, the chance of not flinching is 51.2%, so 51.2% of the time chansey is landing that last blow on houndoom. it's not exactly a "chansey is sure to fail" thing. if chansey goes down with houndoom, then chansey has achieved her job of removing a key threat from the game, which can be crucial if houndoom is the only special sweeper they have. you have limited the loss of your team to just chansey.
He might have meant if Chansey takes 3 Dark Pulses, it's more likely than not to flinch at least once, since the flinch probability is over 50% at that point.
If we're talking Chansey vs. other Pokemon 1 v 1, I find Chansey being able to beat the most surprising things sometimes. Like I've come across Mega Aggron and Mega Aerodactyl before that weren't able to deal over 50% damage to it. I agree with whoever was talking about Superpower Hydreigon as well. A lot of people seem to think it beats Chansey, but as long as you are on high health (in my experience you have to be about 75% or higher) when it first attacks, and Softboiled on the first Superpower, then you will win, since the rest of the Superpowers will do less than 50%.
However, I don't think it's broken, there's still many ways to get past it. I find if Chansey is at high health, it's ridiculously easy to switch in and do whatever, but when it's under around 60%, it starts getting quite difficult to switch in (and when you do, you usually have to prioritize healing yourself over supporting the teammates, and once you've done your double-Softboiled or Wish/Protect or whatever, the opponent has usually switch in something that ruins Chansey, so you have to switch back out again). I always play cautiously with it, always trying to keep it as high on health as possible. It's tempting to predict switches and throw status or a cheeky SToss around, but it's too much of a risk a lot of the time, since a lot of things Chansey can usually beat can force you out if you didn't heal yourself on their switch-in.