Cooks Tavern owner and former Bills offensive coordinator John Kuechly will join the Jets coaching staff.
Kuechli is a longtime Buffalo Bills assistant and has been the offensive coordinator of the Bills since 2015.
He joined the Jets last season as an assistant coach, helping them clinch the AFC East division title and advance to the playoffs.
Kilpatrick is a former Jets assistant and offensive coordinator.
Keshawn Johnson is the Bills No. 3 quarterback, behind Tyrod Taylor and Josh McCown.
Johnson is also the No. 1 offensive lineman, behind Mike Gillislee and Dwayne Allen.
Johnson has made four starts for Buffalo this season.
The Jets are still searching for a replacement for Ryan Fitzpatrick, who retired in September after three seasons.
They signed former Cleveland Browns offensive coordinator Tom Coughlin on Thursday to replace him.