
If there's no option to flirt, keep investigating and asking them questions about themselves. Whenever you find yourself in Haven or Skyhold, talk to any of the companions you want to romance and choose the heart option whenever possible. In order to actually romance any of them and receive the trophy, you'll need to do multiple quests for them. Check the list below for those you can romance. There are a few people who you can flirt with, but not actually romance.

If you don't know where everyone is located, open the area map and hover over the black face icons to see who's where. If you don't see any icons in the middle of the dialogue wheel, go to Options > Interface > Uncheck Hide Tone Icons. In order to romance someone, every time you talk to one of them, you need to choose the dialogue option with a heart icon. Whether you can romance them depends on your character's gender and race. Make sure to obtain this trophy before starting this mission, or manually save before the last mission and finish this trophy afterwards by reloading the save file.

After finishing the last story mission "Doom Upon All The World", you won't be able to romance anyone, or finish any of the romances you had going.
