League of Legends (LoL) Question: Cooldown timers

it is critical that you know your opponents Flash cooldown. When their flash is down, it really hinders the amount of mobility your opponent has, as well as diminishing his presence in a lane.

If you have flash and they don't, this and the previous factor compound, giving you massive presence in lane (provided that the lane was initially neutral).

When I jungle, I am incentivized to camp a lane knowing that their flash is down. It's quite easy to attempt 2-3 ganks on them before their flash comes back up. It's not particularly hard to do - just type in chat: Twitch flash (time)+5. Everyone will know what you mean.

I'd say the other critical summoner spells you need to document, are Teleport cooldowns, and during the early game, Heal CD. Ultimates are good to make a mental note of if the cooldown is long, but are not always to necessary to track thoroughly.

I would say yes, when it comes to ultimates that have long cooldowns.For example, if you're playing against a Warwick and he ganks your lane and uses his ult on you it's good to call out "WW no ult" so your other lanes know they have a gap in which they can play more aggressive without having to be afraid of getting locked up by Warwick. As said before Flash is extremely useful to time since it opens up a space in which your lane opponent is down an escape. Other than summoner spells and big ultimates theres not much else important to time.

Another thing you can time is wards. It's a little harder now since you have to pay closer attention to what ward the enemy is using (ie: trinket, green, pink) since they last different times but if you enable timestamps on messages you can use a ping, like a danger ping, that shows up in chat right when they place a ward. Simple trick but it allows you to get an accurate timer on the ward, down to the second

For me there are too scenarios: As a top or mid laner I'd instruct the jungler about my opponent's flash being down and on bot lane as a support I can make such notes because I'm not forced to concentrate on last-hitting.
Ofc you can note these timers but I generally don't see anyone doing this since the addition of jungle buff timers. Tbh it would be pretty helpful to know the exact timer on their AD Carry's Flash or their AP Carry's Zhonya's Hourglass but I haven't seen anyone favoring it so gar and personally I'm just too lazy. I guess I focus more decent and favorable situations to team fight than on not hesitating to start a trade when someone's summoner spells done. In the pro scene they're are obviously instrucing each other about such information and the result is being pretty successful. Just test it on your own and you will experience on how your team members will react to it and use these hints.