Its simple
They're all going to feed lmao.
I play mid though so its a little different.
When the jungler ganks me, and I see him go to the bot side jungle after he fails or succeeds, I know he's likely going to clear and head bot, or go straight to bot. Than combined if bot isn't warded, then I'm gonna want to shove and get ready to roam down there.
I'm also trying to ward and get vision of the enemy jungler when I have time, either by warding entrances/camps, placing a control ward in his jg, or hitting the vision plant. When he's not one side, and the other side is gankable, then I want to start heading over there.
I take TP sometimes, so just using it when bot or top is getting ganked can be pretty good.
In other wards, just try to track the enemy jungler and fight with your team.
To do any of this though, you have to be winning and having control over your lane, preferably already having killed him and playing a carry champion.
Sometimes I don't even have to do any of this, and there is just enough time to run from mid to bot before the people that are low get away.
I looked at your champs. Kayle isnt going to be able to do this too well like a quinn could. You still want to TP and potentially try to turn a fight though. I see that some of your games, you have very low kill participation, like one or two because your team feeds and you just dont bother with them. You gotta use that TP earlier. Dont use it to return to lane if you dont have to. If you aren't taking TP for cross map plays/flanks, then I suggest just not taking it period. If you're confident that you can get early kills and dominate your lane, then take ignite.
If you're confident in your kayle, then I think you should try playing her mid. You will just have more pressure on the map as a midlaner, since pushing and roaming is alot easier. Idk how kayle mid is, but mid in general is just easier to carry with. Maybe try quinn mid unless you need an AP. People played Quinn mid (pretty sure in LCS too? Not sure) when she was meta/really strong.
On shyvanna, if you know your bot is going to get ganked because nothing is warded, they're pushed, and you know their jungler is bot side, then do a lane gank. Walk from your tower into the bushes. This is probably the easiest way to get ganks off imo.