Delfouneso scored the opener before the break but goals Flynn and substitute Davies gave United the three points.
Steven Pressley named an unchanged side from last week’s draw with Wolves, and the Sky Blues kept the ball well when in possession in the opening 20 minutes. Conor Thomas was booked for a late challenge on Stefan Scougall after 21 minutes, and shortly after Callum Wilson nearly nicked the ball off United goalkeeper Mark Howard, but the ‘keeper cleared in the nick of time as the striker was closing to robbing the ball from him in the penalty area.
The Blades created the first clear chance, when Michael Doyle’s header from Jose Baxter’s cross was saved comfortably by Joe Murphy.
But the opener came on 39 minutes when John Fleck surged through the Blades midfield and played in Delfouneso who shrugged off two challenges to calmly finish past the onrushing Howard.
Wilson could’ve doubled City’s advantage when he lashed an effort straight at the ‘keeper from just inside the area. Fleck, who was instrumental in City’s opener was booked just before the half-time whistle after a mistimed tackle on Jamie Murphy.
United started the second-half with purpose and John Brayford raced through but Murphy was alert to stop the defender’s effort with his legs. Brayford missed another good chance soon after when he blazed over from ten-yards out.
But United made their chances pay when Conor Coady and Flynn combined on the right-hand side and swapped passes to free Flynn inside the and he tucked the ball past Murphy in from eight-yards out.
City then had a penalty appeal turned down when Mark Marshall’s cross from the left looked as though it was handled by a United defender.
The Sky Blues fell behind when Coady ran at the heart of the Coventry defence and found substitute Ben Davies unmarked and he finished inside the area.
Pressley then brought on Carl Baker for Conor Thomas in an attempt to take a share of the spoils, but United continued to press and Neill Collins headed over from four-yards out.
Nathan Eccleston was brought on for David Prutton with six minutes to play in an attacking move shortly before Marshall came close to an equaliser, when his vicious shot inside the area flew narrowly over. But the Sky Blues could not force a leveller as the Blades saw out four minutes of added time to take all the points on the last day of the season.
Attendance: 20,723 (1,769 Sky Blue Army)
Coventry City: Murphy (c), Christie, Webster, Willis, Clarke, Fleck, Thomas (Baker 77), Prutton (Eccleston 85) Marshall, Wilson, Delfouneso
Subs: Burge (GK), Adams, McGeouch, Seaborne, Finch
Sheffield United: Howard, Brayford, Maguire, Flynn, Doyle (c), Baxter (Davies 65), Collins, Coady, Scougall (Porter 45), Murphy, Freeman (Hill 87)
Subs: Long (GK), McGinn, Paynter, Dimalo