Flournoy played 54 of the Cowboys' 83 snaps on offense and finished with two catches for 19 yards on three targets in Monday's 34-10 loss to the Texans.
Flournoy caught one of two targets for 13 yards in Sunday's loss to the Falcons.
Flournoy caught his only target for 12 yards in Sunday's loss to the Lions.
Flournoy (coach's decision) is inactive Sunday against the Browns, Jon Machota of The Athletic reports.
Flournoy caught all three of his targets for 30 yards and a touchdown in Saturday's preseason loss to the Chargers.
Cowboys coach Mike McCarthy said Sunday that Flournoy is day-to-day with a knee injury, Calvin Watkins of The Dallas Morning News reports.