Getting Acquaintances to become Friends
Some times when you trade with an acquaintance you get a prompt asking if you want to be friends with the other person. Most of the times it does not. It happens randomly too. It could be after the first trade after just trading 1 pokemon or it could happen after the 3rd trade request with that person after trading 10 pokemon.
When and how can I get the friend request to appear?
One Solution collect form web for “Getting Acquaintances to become Friends”
According to Bulbapedia:
The main window of the PSS divides other players in three categories: Friends, Acquaintances, and Passersby. A Passerby will automatically become an Acquaintance if a Battle or Trade (including Wonder Trades ) is made with him/her: after trading or battling with a player already in the Acquaintances, a prompt to add them to the Friends group will appear.
So it seems that 2 Battle/Trades are needed in order to get the prompt.