It looks like you get more healing per flask from casting 3x Heal Aid or whatever it's called, and chugging an Ashen Estus, than just drinking a regular Estus. If you're patient enough to stand there and spam heals after fights, it's an economically sound approach if one has trouble getting from one bonfire to the next. Every class starts with 10+ attunement except for warrior, so all the other ones can attune one spell without needing to invest any points in it, and all but sorcerer have the 8 faith required to cast this spell.
It doesn't appear to matter whether or not you have the 10 faith that the talisman requires; you can cast the spell regardless, I think it just affects damage spells. Both the spell and talisman can be bought from the old lady in Firelink Shrine, and if you split your flasks 2:1 for regular and mana, you've got enough regular ones for in-combat use. It's probably not something experienced Souls players need to fuck around with, but it's an option for struggling newcomers.
It feels like you get about 30-40% more healing out of Ashen Estus + healing spells, but this may only last until you get to upgrade the flasks as the Ashen Estus pretty much fills the FP bar of a 10 attunement character even at base level, and therefore doesn't really benefit from being upgraded.