Finnick didn't think he'd ever have kids, and couldn't really imagine anyone wanting to have a child with him anyway. He'd put the possibility out of his mind at home, due to the probability of any child of his being reaped for the games. Of course that couldn't happen here, but he still didn't really think about having a child. He was still the same person with the same damage, and surely that wasn't a realistic possibility for someone like him.
But if Briseis wanted that, then he wanted it for her. She deserved to be happy here.
"I'm sure Arva will grant you that. Did someone explain how it works here? Apparently if you both want it, then it happens, simple as that." He smiled at her. "So as long as Scott agrees, it will happen for you."
Maybe he could be funny uncle Finnick to her kids. That sounded nice.