How would the game track this aside from flat out violating a player's privacy and asking to know their sexual preference?
They could track the LI to whom the character flirts until that encounter + 2 desire demons.
If the character flirts only with females => 2 female Desire Demons
If the character flirts only with males => 2 male Desire Demons
If the character flirts with both females and males (or with no one) => One male and one female Desire Demon.
That's how I think they would resolve this issue if they ever think of implementing a Desire Demon interaction that is more complex than " There's the Desire Demon. Let's kill it! " . As for the fight, don't talk situations...just mix them.