Kidlington's goal was scored by Lewis Coyle (pictured) but earlier goals from Thomas James-Peddler and a brace from Dan Rapley saw the visitors home.
The damage was done in the first 20 minutes when Flackwell established a two goal lead.
However a spirited fightback lead by Lewis Coyle and Jack Quainton had Flackwell on the back foot for most of the second half.
Kidlington applied a lot of pressure but the Flackwell defence held firm until Coyle struck in the 84th minute.
Very late in the match substitute Rob Johnson was felled in the area and Kidlington were awarded a penalty, Ryan Curtin took it, but it was well saved by the visitors keeper.
All in all the best team on the day took the points, but Kidlington played their part once again in a very entertaining match at Yarnton Road.
Kidlington now move on to play Wantage in the FA Cup this coming Friday eventing, k.o.7;45 at Alfredian Park.
COYG