SWTOR’s first officially marketed ‘same sex’ flirt/romance options were included in Rise of the Hutt Cartel’s Makeb Planet with Lord Cytherat for Imperial male characters and Lemda Avesta for Republic female characters.
However the game was heavily criticised for not including any other romance options or flirts in existing or newer game content until the release of the Bounty Brokers Association/Death Mark Event (Bounty Hunting Event) in SWTOR. In this event any player class can hunt several bounties across numerous Vanilla-game planets from Dromund Kaas to Voss and Coruscant.

Once you have collected 4 pieces of Intel from the planets cantina, you can rendezvous with a Bounty Contact NPC, the game will give you one of several human or alien male and female characters, each of these Bounty Contact NPCs offer a special [Flirt] option based on being hetero or same-sex, you are also able to exit the cutscene and re-open it to generate a different character with their own flirt options and dialogue before you continue on with completing the Quest.

Since the Bounty event can be started by characters at least level 15 that can access Coruscant or Dromund Kaas, this makes these dialogue encounters the earliest in the games timeline that a character can initiate same-sex / bisexual romance/flirt options with a character in the game.