He played college football for the Florida Gators and was signed by the Philadelphia Eagles as an undrafted rookie free agent in 2014, and he won Super Bowl LII with the team in his final season with the Eagles, including helping execute the Philly Special.

[4] As a freshman in 2010, he broke Tim Tebow's team record for touchdowns in a single game with six in a 48–14 victory over Kentucky.

Standing at 6'2", he tied Tennessee State's A. C. Leonard as the shortest tight ends at the combine and was the lightest by 11 lbs.

Burton finished with the fastest 40-yard dash time, tied for second in the three-cone drill, and fourth in the short shuttle among his position group at the combine.

[8] On March 17, 2014, Burton opted to participate at Florida's pro day, along with Dominique Easley, Solomon Patton, Loucheiz Purifoy, Marcus Roberson, Jon Halapio, Jonotthan Harrison, Ronald Powell, Jaylen Watkins, and two other teammates.

Burton lowered his time in the short shuttle and three-cone drill, while also increasing his broad and vertical jumps from the combine.

[9] At the conclusion of the pre-draft process, Burton was projected to be a seventh round pick or be a priority undrafted free agent by NFL draft experts and analysts.

[13] Throughout training camp, Burton competed for a roster spot against James Casey, Emil Igwenagu, and Blake Annen.

Head coach Chip Kelly named Burton the fourth tight end on the Eagles' depth chart, behind Zach Ertz, Brent Celek, and James Casey.

[14] The Eagles initially had three roster spots for tight ends, but decided to make Burton the fourth after determining it was too risky to place him on waivers.

Burton completed his rookie season with a total of four combined tackles on special teams and five carries for 10-yards and a touchdown in 15 games and zero starts.

[19] Burton entered training camp competing for a roster spot against Eric Tomlinson, Andrew Gleichert, and Justin Tukes.

[21] On August 29, 2015, Burton caught four passes for 21-yards and two touchdown receptions during a 39–26 preseason victory at the Green Bay Packers.

[19] Burton was able to showcase his abilities after having increased playing time after Zach Ertz missed the preseason after suffering a core muscle injury.

On November 26, 2015, Burton recorded his first career reception and finished with two catches for 49-yards, though the Eagles lost 45–14 at the Detroit Lions.

[23] He was a key special teams contributor and led them with 19 combined tackles and also caught three receptions for 54 receiving yards in 16 games and zero starts.

[28] On September 19, 2016, Burton caught five passes for 49-yards and scored his first career touchdown reception during a 29–14 victory at the Chicago Bears.

[29] On October 16, 2016, Burton earned his first career start and made one catch for a seven-yard gain as the Eagles lost 27–20 at the Washington Redskins.

During a Week 14 matchup against the Redskins, Burton caught a season-high seven passes for 65 receiving yards in the Eagles 27–22 loss.

[37] In Super Bowl LII against the New England Patriots, Burton threw a touchdown pass on the famous Philly Special trick play to quarterback Nick Foles with 34 seconds remaining in the first half.