Let's see, over a 3-year period there was Miramanee, Deela and Drusilla. That's three times.* Carol, Ruth, Janet Lester, Janet Wallace and Areel Shaw were all old flames, but none of them were presented as one night stands. There was a lot of kissy-face, but that's as far as most of his interactions went during the time of the original series.
*An argument can and has been made for Edith Keeler given Kirk's feelings for her, but there's nothing presented in the episode to indicate they ever went that far.