You guy's aren't really competing over anything, so Kohaku does not need to make a counter-roll for Saki's affection. If you want to flatter another maid you'll have to role-play it.
The closest thing to using affection on another player would be the optional seduction rules. One player uses affection/cunning in attempt to seduce someone, and the defender rolls their affection/cunning in response. However, we're not doing the whole seduction thing because it makes everything complicated.
Roguelike, here's your item. Looks like you just have to read a letter to yourself (or out loud) and you'll stop yourself from having a stress explosion. Since we can't actually 'give a speech', just write more than 3 or sentences.