When can I kindle bonfire to more than 10 estus flasks?

You will defeat a certain boss shortly after about, I'd say, halfway through. When you see 'right of kindling acquired' then I believe yo can go to 20 flasks at a bonfire for three humanity. When you start a NG+, that bonfire would remained kindled as well.

^^That's right. I pretty much went and kindled all of the useful bonfires to 15 or 20 right before I finished my 1st playthrough.

Thank you for the info.  Time to tackle a couple of gargoyles.

To kindle to 20 flasks do you use 3 humanity and then just kindle once or do you use 2 humanity then kindle and then use 1 more humanity and kindle again?

There's a boss deep in the catacombs that will drop the rite of kindling that will let you do it. I don't suggest going down there until your around lvl 40-50, there are necromancer that keep reviving the skeletons down there you have to kill them to stop them, you can use a divine weapon on the skeletons to stop them from getting up but to stop it permanently you have to kill the necros. Once you kill the necros they don't spawn back

[quote user="GunnyDawg21"]There's a boss deep in the catacombs that will drop the rite of kindling that will let you do it. I don't suggest going down there until your around lvl 40-50[/quote]It's totally possible if you're a faith character to go down there at less than level 20, considering you made yourself a divine weapon already. I go down there all the time now around level 10 without faith characters.

I usually go and fight that boss first even, before fighting the tarus demon. I know a couple short cuts. Jumping down that pit in the center, and you can bypass most of the level and fall right into the area here the rolling skelentons are. the boss name is PINWHEEL. and its a pretty weak boss too. even at level 10 or so, still kicks it's @$$