[2] Dunham attended Pendleton Heights High School, where he measured 5 feet 10 inches (1.78 m) as a freshman.

[3] In his senior season, Dunham averaged 29.5 points per game and shot 92.1% from the free throw line, leading the state of Indiana in both categories.

Dunham was named Madison County Player of the Year as a senior after leading Pendleton Heights to a 23–3 record.

He holds the record for the all-time leading scorer at Pendleton Heights with 1,899 points and led the Arabians to back-to-back sectional titles.

"[7] In ESPN's scouting report, Dunham was listed as the 78th best overall player, due in large part to the fact that what he "does really well is shoot the basketball.

[9] Butler head coach Brad Stevens said, "the thing he brings is an incredible ability to put the ball through the net.

[10] Dunham began practicing basketball drills late at night thanks to senior Rotnei Clarke, and the two became fast friends.

[11] During the 2012 Maui Invitational Tournament in 2012, Dunham had one of his best games as a freshman as Butler routed the then #9 team in the country, North Carolina, shooting 56% (5 of 9) from 3-point range and scoring 17 points.

[14] In a game against #8 Gonzaga on January 19, 2013, that was featured on ESPN's College GameDay, he was the second leading scorer, shooting 4 of 8 from three-point range, behind 20 points and a buzzer-beating floater from Roosevelt Jones.

[18] "Most guys are relaxed, but I look up and I see Kellen, and he's ... going 110 miles an hour," said 2013–14 Butler Bulldogs first year head coach Brandon Miller during an August overseas basketball tour.

"[2] Dunham scored a career-high 32 points against Washington State in the Old Spice Classic, a tournament record.

[2] He was named Big East Player of the Week on December 16 after contributing 25 points to lead Butler past the Purdue Boilermakers, 76–70 in the Crossroads Classic.

[20] Dunham had 30 points in a 99–94 double overtime loss to DePaul on January 9 and tied his career-best with six three-pointers, all of which came in the second half.

[22] Despite his improvements, Butler had a lackluster season, finishing with a 14–17 overall record and bowing out to Seton Hall in the Big East tournament.

[24] Coach Brandon Miller took a medical leave of absence before the season and did not return; he was replaced by Chris Holtmann.

[31] In the Round of 64 of the NCAA Tournament, Dunham scored 20 points, including an important 3-pointer with 1:18 remaining, to propel Butler to a 56–48 victory over the Texas Longhorns.

[46] On October 21, 2018, Dunham was named to the training camp roster of the Capital City Go-Go of the NBA G League.

[47] Playing for the Go-Go, Dunham developed into one of the best three-point shooters in the G League, with the majority of his shots coming from behind the arc.

[48] On February 13, 2019, Dunham tallied 19 points, four rebounds, one assist and one steal in a win over the Westchester Knicks.

[53] Dunham signed up to play for the Pendleton Legends, part of the Hoosier Hardwood Basketball Association, a league headed by former Indiana University great Kent Benson for the 2021 season.