You can keep looking at Stories as long as one side hasn't blocked or passed on the other. And sharing your Stories doesn't change your sharing settings in Facebook or Instagram -- you don't have to worry about widening access to your account just to woo someone.
This isn't a novelty. Tinder is incorporating Snapchat Stories, and Bumble is no stranger to disappearing videos either. It's also been possible to link your Instagram account to Tinder. However, this does show that Facebook is determined to make its dating service competitive, if just by exploiting the vast tools it already has at its disposal.