What is the limit of Estus flasks?
No, you cannot have more than 20 flask charges.
You will have 20 charges after resting at +3 Bonfire (Kindled 3 times).
However, you can get extra charge if some other player kindles a bonfire in the same area. So effectively you can use more than 20 flasks after resting at bonfire, but you cannot carry more than 20 at the same time.