Oh, ok. When you plus it you're just upping how much it heals. You get additional flasks by kindling bonfires with humanity. Until you beat the Catacombs you can only do this to 10, after that it will go to 20.
The Firelink Shrines bonfire should be at 10, any other will start off at 5.
You can get one in Blighttown, Duke's Archives, killing the Daughter of Chaos, killing the firekeeper of Anor Londo, and defeating Lautrec after you invade with the Black Orb.