In general you want to be pressing these cooldowns on CD if there is any damage going out. This means if you're Kyrian, in a 5 minute fight you should have 3 Wings casts and 5 Divine Tolls. Holy Paladins are a cooldown class and we rely on using them as much as possible for throughput. It heals for more and the heals goes out instantly instead of having to wait for the cast. If you need an emergency heal because someone is going to die in the next GCD and you don't have Holy Shock or Word of Glory available, use Light of the Martyr instead of Flash of Light. You should only ever use this on your beacon target to generate Holy Power when you're unable to be in melee for a few seconds and have no infusion proc, or you're just filling empty GCDs (everything else is on cooldown). This is prevalent in both Mythic+ and raid, and in either situation will completely gut your healing. One of the most common mistakes I see from Holy Paladins when reviewing logs is that players often fall back on spamming Flash of Light for healing. This means if you have one charge of Crusader Strike on cooldown and you're one GCD away from having Holy Shock back up, you should fill with a different ability (like a holy power spender, judgment, hammer of wrath, etc), then use Holy Shock, then use your Crusader Strike so that you get the Holy Power AND the Holy Shock cooldown reduction. I'll mention here as well that proper crusader strike usage is important for getting the most out of Holy Shock when running the Crusader's Might talent, which makes Crusader Strike reset the cooldown of Holy Shock by 1 second. Any time you have Holy Shock available you should be prioritizing it over any other spell you have (unless you are at 5 Holy Power, in which case you should use a Holy Power spender, then press Holy Shock).
The most common issue I see is of players not using Holy Shock when it's available. If there is absolutely no damage going out and everyone is topped, just throw WoGs on the active tank or use Shield of the Righteous for damage. Doing this will absolutely hemorrhage your hps, so make sure you're spending your Holy Power as you generate it. The worst thing you can do as a Holy Paladin is overcap your Holy Power (meaning use a Holy Power generator when you already have 5 Holy Power).