Living water flowing from believers refers to the Spirit.

John 7:37–39

³⁷In the last day, that great day of the feast, Jesus stood and cried, saying, If any man thirst, let him come unto me, and drink.

³⁸He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of living water.

³⁹(But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified.)