You can talk to Breezestar at midnight, when you've talk enough with her she'll invite you to Fireclan where you can speak to fireclan members (And if you're her mate you can adopt two kittens there)
Well. After she's invited you (And you're hopefully a she-cat) to Fireclan and you speak with the cat who she thinks is your dad press on her and she should say something like "We got a problem" and then the kits should appear and she'll ask if you want to adopt them. Sorry if I'm bad at explaining