When you use a inventory Humanity it is added to your counter. These are like souls and are lost if not recollected after dead. You can kindle fires (get more estus flasks) or reverse hollowing (go human) using humanity in your counter. If your trying to go human you need a minimum of one but to kindle you'll need to be human so if you are hollow you will need to add 2 humanities to your counter. Counter- humanities are received when defeating a boss as a summon. Hope this helps

Also, the only way to upgrade your estus flask is with firekeepers souls. You must mean kindling? Humanity is not required to reinforce estus flask (talk to Anastacia of Firelink Shrine behind Firelink Bonfire)

You can get it in your counter by using the Humanity item, or by killing a monster in a level you haven't completed. (It will automatically be added to your counter.)

The Humanity item adds one humanity.
The twin humanity item adds 2 humanity.
Beating a boss adds one humanity. (This includes if you have been summoned to help with a boss)
Invading a player successfully, or defeating an invader adds one humanity.
Getting your messages ranked up can add humanity.

Carrying humanity in your counter will increase your drop rate, but you can lose them like souls if you die and do not retrieve your bloodstain.
Reversing hollowing lets you summon players to help you, but you can be invaded.
Kindling increases the number of estus flasks the fire gives to you. Some fires, like in firelink shrine, are already kindled once. You cannot kindle more than once until later in the game. You must be human to kindle.