They never become 'partners' at the end of any game. Once or twice it is suggested but Link never says 'will you go out with me?' Or anything of the sort. The closest to anything like that is Zelda moves towards Link at the end of AoL suggesting she will kiss him, but then the curtain comes down and we never see a kiss of the sort she could just be going to walk past him or anything. So no, they never become partners.
I think you are forgetting something important. At the end of the Oracles games, Zelda actually kisses Link. Yes! But I think she kisses Link because he just saved the land of Holodrum and Labrynna.
Like in your signature!: + = <3