No. 1 - Devonte' Graham, 78.7%, 2014-2018
Like his teammate Frank Mason, Graham was also originally headed to a smaller school, Appalachian State, before being plucked by Bill Self. Like Mason, Graham also became a first-team All-American.
Not surprisingly, since they overlapped a couple of years, but KU was very successful during Graham's tenure, winning 122 games. During the two seasons they played together, Mason and Graham won 64 games, and went 31-5 in the Big 12.
As a free throw shooter, Graham solidified himself as the best in Kansas basketball history, making 362 out of 460. During his final campaign as a Jayhawk, he made 167 free throws out of 202 attempts, good for 82.7%
He scored 1,750 points and averaged 3.1 rebounds, 4.5 assists, and 1.4 steals at Kansas. He has gone on to a successful NBA career and will be remembered as being one of the best Jayhawks in this century.
All statistics gathered from Sports Reference