Barnsley manager Flitcroft was axed moments their woeful 3-0 defeat at Oakwell to Birmingham Saturday night.
Over on the west coast, Owls chief Jones was clinging to his job after a 2-0 loss at Blackpool left them joint bottom of the Championship with Barnsley on 11 points.
That is six points adrift of safety and the South Yorkshire rivals face huge tests to escape the drop for the second successive season.
Flitcroft was coming up to his first anniversary in charge, after replacing Keith Hill in December, 2012, but Barnsley have won just twice in 17 league games this season.
“Barnsley Football Club can confirm first team manager David Flitcroft has been relieved of his position at the football club,” read an Oakwell statement.
“Technical coach Martin Scott and strength and conditioning coach Guy Proctor have also parted company with the club.
“Assistant manager Micky Mellon has been placed in caretaker charge of first-team affairs, assisted by development coach Paul Heckingbottom in the meantime.”
Goals from Paul Caddis (2) and Nikola Zigic did the damage to send the majority of the 10,077 crowd home miserable.
The club say they will make no further statement until Wednesday, with a trip to Brighton tomorrow night to prepare for.
The statement concluded: “The club would like to place on record their appreciation and thanks for what David, Martin and Guy have achieved.”
Former Portsmouth manager Michael Appleton is 5-2 bookies favourite, but Sean O’Driscoll – the former Doncaster Rovers manager – is highly regarded at Oakwell and could be a contender after leaving Bristol City last week.
As for Wednesday, they have only won once in 16 Championship outings and pressure is mounting on chairman Milan Mandaric to wield the axe.
Owls fans jeered ‘Jones out’ and ‘You’re getting sacked in the morning’ after defeat at Bloomfield Road.
Wednesday face a Hillsborough double-header against Championship leaders Leicester City tomorrow night and Nottingham Forest on Saturday.
Jones is adamant the revolving managerial door at Hillsborough must stop if the club want stability and long-term success.
“This club over the last 10 years has had something like 12 or 13 managers but sacking managers isn’t the answer,” said Jones.
“I am fighting for my life, my staff are fighting for their lives. Players need to take responsibility... if they get an open goal, they have to put it in the back of the net.”
Ricardo Fuller pounced in the sixth minute, punishing slack defending at a corner, and the Owls spurned three gilt-edged chances to level. Dan Gosling’s second-half effort killed the game.
“We were probably the better team, but you have to put chances away,” said Jones. “I speak to the chairman (Mandaric) every day. Is he happy? No. Am I happy? No. Should players take responsability a little bit more? Yes.
“Nobody has a magic wand, no magic formula, apart from hard work, determination and more importantly, don’t be fearful.
“I think at the moment we have one or two just having a little bit of fear mode. We can’t get any lower, so what’s to fear, what are they frightened of?”
Former Owls left-back Tommy Spurr was the match-winner as Leeds United’s good run ended with a 1-0 loss at Blackburn.
Doncaster Rovers and Huddersfield Town pulled off tremendous 2-1 wins against promotion chasing QPR and Burnley, respectively.