During the second half of the Scotland international match, Select Car Leasing collapsed at the stadium with no one around him, causing great concern among players, coaches and fans.
Fleck received lengthy medical treatment and was then pulled into a waiting ambulance after helping his legs with an oxygen mask.
After the game, Sheffield United boss Slavisa Djokanovic confirmed the 30-year-old was conscious and speaking in hospital, with a further update expected on Wednesday morning.
Djokanovic said: “John is conscious, he is in the hospital, he is talking to doctors and he is in good hands.
“We hope that everything will be fine and we hope that everything will be fine. He was talking and he asked for the result.
“I didn’t actually witness the incident, but it looked like he just collapsed, without any physical contact with his surroundings.
“I am not a doctor but the news is positive. It was not an easy situation for everyone.”
Regarding the Flake incident, Reading manager Veljko Paunovic said: “The experience we all experienced tonight was so dramatic and so terrifying.
“I hope John returns to his normal life in good shape as soon as possible, and plays football like never before.
“Hopefully, there are no other consequences [for him] After this.”
Sheffield United won the match 1–0, thanks to a second half effort from Jaden Bogle.