Kayle can't oneshot for shizzle, her dps is fast but is reactable and the issue is that she wins trades and enables high damage team mates with her ult.
I'm sorry though but if you were 7/0 and 15/2 on botlane than you had all the means to keep kayle under focus, she suffers burst and CCs because of how squishy she is, I think that the major issue was that you didn't care to keep her in check and ultimately lost because of it.
Hypercarries need to be checked in place until you win, that's how it works.
Edit:
I took a look at your match history and what I noticed is that your enemies also had a 11/4 Veigar and a lot of CCs while your only hard CC were you with Vel'koz and Braum (which can be easily avoided), they had Thresh, Jarvan and Veigar all of which can synergize pretty well. You had a game-winning teamfight right before their comeback and yet all you achieved was one inibitor out of it with Khazix and Vayne still alive. Then you go Elder while the enemies picked a Baron, I don't know if your team split but you did the wrong choice or you got outplayed. The fights after are a big reason you lost, you focused down the unfed enemies while letting Veigar have his way which in combo with a lategame Kayle is a death sentence.