I am asking because one of my friend's way back in the past during an earlier generation of Pokemon said he got his slowking by trading a slowbro while it was holding a king's rock.
No. Slowbro and Slowking are the final evolutions of the Slowpoke. One cannot evolve into another.
Slowpoke evolves into Slowbro at level 37.
Slowking evolves when a Slowpoke is traded while holding a King's Rock (it won't work with Slowbro).