Do phytoestrogens have the potential to increase estrogen levels, and what mechanisms underlie their effects on hormonal balance in the body?

The answer is no, not more than you already have in your body.

Phytoestrogens only block receptors for bad estrogen, which automatically raise your relative good estrogen. BUT it will not increase your levels more than you already have. So consuming flax oil or seeds for example are safe for men and women.