Both players had been waived, but because the waivers were not processed until 4 p.m., the teams had the opportunity to complete the trade.
As Auburn's kicker in 2013, Parkey led college football with 69 touchbacks. He also made 15 of 21 field goals.
Philadelphia's incumbent kicker, Alex Henery, made 23 of 28 field goals last season.
Fluellen is an undrafted rookie free agent out of Toledo. During his senior year in college, Fluellen posted 1,336 yards from scrimmage and scored 10 TDs.
- Alex Hampl