Graham had not scored since leaving the Liberty Stadium earlier this year, but he returned to haunt his former club with a fine far-post finish in just the eighth minute.
Hull kept their hosts at bay with ease until the hour mark when Jonjo Shelvey's driven ball hit Flores and flew in to give the Spaniard his first Premier League goal, although replays suggested the ball had come off his arm on the way into the net.
Hull could still have won had the referee Martin Atkinson not missed a blatant handball by Swansea defender Dwight Tiendalli as he blocked an Alex Bruce header.
Michael Laudrup, the Swansea manager, was satisfied with his team's point which takes them into 10th place, three points behind Manchester United. "I think it's a fair point, I have to say. It wasn't a very good game to watch. The first half we played and played and played but it was much too slow and there was no pace on the ball, so it was quite easy for Hull to control and to defend.
"They got a goal, a good goal. It was a good cross and a good finish from Danny. In the second half we did much better, much quicker and we got the equaliser and we had a chance maybe for a second goal, a good chance from Michu but I think after the first half we did not deserve to win this game today."
Referring to the alleged handball of Flores for the equaliser, Laudrup added: "It's into his body so it's not that he's using his hand to score. I don't know if it's touched both his leg and hand."
Hull have collected four points from their last three matches, which has the nod of approval from their manager, Steve Bruce. "In the Premier League, a newly promoted team coming away from home to get a point, you're always satisfied with it. We've played eight or nine of the top 10 teams away from home, so it's been a difficult start in that respect. We're in the pack and just below halfway and, after 15-16 games, that's very pleasing."