They were quite often seen together in public after Friends with Benefits was released in summer 2012, and they were quite affectionate with each other but, as far as could be seen, mainly in a jokey way. They certainly never claimed to be in a relationship and it's not unusual for the two stars of a film, especially a romcom, to let themselves be seen together in public for a while afterwards to generate publicity for the film.
As Justin Timberlake married his long-time girlfried Jessica Biel only a few months after these stories began to appear, it seems most likely that there was nothing serious going on with Mila Kunis. She is also now involved with Ashton Kuchta and there have even been rumours that they may be expecting a child.
The wedding was a big one and got a lot of publicity, especially as Justin apparently sang a song for his bride.