This page contains all the information you need on how to have a romance with Jack.
Jack is a romance option only available to Male Shepard if she survived the Suicide Mission in Mass Effect 2. Before you consider romancing her, you’ll need to complete the mission, Priority: Palaven. This will unlock the Side Mission, Grissom Academy: Emergency Evacuation .
Once you’ve completed the mission, go to the Purgatory at the Citadel to continue the romance with Jack. During the conversation you’ll want to say “I still want you”. There is not much else involving Jack from this point onwards, but you’ll have some cutscenes with Jack during the Citadel DLC.