Hull took the lead after nine minutes as former Swansea man Danny Graham scored his first goal since leaving the Welsh club back in January.
Swansea, looking for consecutive league wins for the first time this season, laboured in the final third for much of the contest despite dominating possession.
Yet the hosts received a stroke of fortune on the hour mark as a Flores goal was allowed to stand, despite the ball appearing to strike the hand of the Spanish defender.
Hull fashioned the better opportunities in the closing stages and saw a David Meyler goal disallowed for offside before the game was brought to a close.
Both sides move up a place in the table, with Swansea climbing to 10th and Hull - a point worse off - leapfrogging Stoke City into 12th.
Michu returned from a five-week injury lay-off in one of three changes to Swansea’s side, while goalkeeper Michel Vorm missed out with a recurrence of a knee problem.
Curtis Davies was back from suspension for Hull and replaced Robbie Brady.
Graham struck with the game's first real chance, the Sunderland loanee beating Flores to Ahmed Elmohamady's far-post cross after Ashley Williams had passed the ball straight into the path of the Egyptian.
Swansea dominated possession for much of the first half without creating much in the way of chances as Hull produced a stout defensive display.
However, defender Ben Davies perhaps should have done better when he fired over from the edge of the area following neat work from the hosts.
Swansea began to exert more pressure in the opening stages of the second half, and were rewarded when Flores levelled.
The 26-year-old appeared to turn home Shelvey's left-wing free-kick with his arm, but referee Chris Foy allowed the goal to stand.
Goalscorer Graham was replaced by Robert Koren soon after - the ex-Watford man holding his back as he left the field - but Hull continued to create opportunities.
After an appeal for handball in the area against Dwight Tiendalli had gone unanswered, a tight offside call denied Meyler a goal and Tremmel then displayed excellent reflexes to deny Yannick Sagbo from distance.
Michu went close for Swansea at the other end, forcing a strong stop from Allan McGregor, but that proved to be the last meaningful chance of a match that ended with a flurry of late bookings.
