I'm coming from Bloodborne, never played a Dark Souls before and I'm looking to make my entry in this one.
I have a question, we only got 3 flasks as opposed to the 20 blood vials in Bloodborne? That must make the game considerably more challenging.
Like everyone said, you get more. Actually in Dark Souls 1, if you kindle a bonfire once (easy to do) you get 10 flasks when resting, which is quite generous. Most of the time you'll be dead or on your way back to the bonfire before you run out. You can get 20 max if you kindle the same bonfire two more times when you get a later item. Dark Souls 2 handled flasks differently and also gave you Lifegems (regen items).
In BB though, they definitely made things a lot easier in regards to healing. The items are consumable but you can still hold 20 vials from the start. You can also use them faster than flasks, and the healing is instantaneous in comparison to Dark Souls 2. Plus vials also had a dedicated button so you won't be fumbling and scrolling through your equipped items to get to the flask when you need it.