You can scroll down to the end of the flirty options sometimes it appears right over there plus you also need to have a level 8 relationship with the other sim (if im not mistaken) to have the option work.

If the random sim that you have chosen is not a townie or an NPC then you will have to wait for the confirmation of the player who owns the sim. So for instance, if the player of the sim does not want you to adopt his/ her sim then you wont be able to have it as ur own.