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Kennett, a former Waitaki Boys' High School pupil, was fourth fastest in heats of the 4000m individual pursuit in an excellent time of 4min 28.128sec.
He battled hard in the medal ride against Spain's David Muntaner Juaneda at the Sir Chris Hoy Velodrome in Glasgow.
It was the first time the 17-year-old world junior championship silver medallist had competed over the 4000m distance in open competition.
Muntaner Juaneda clocked 4min 28.429sec in the medal ride, while Kennett managed 4min 31.987sec.
"Backing up at this level was the challenge for a young rider like Dylan. He didn't have the legs in the final and was not able to get on schedule from start," BikeNZ coach Dayle Cheatley said.
"He showed good fight in the last kilo and I think he can be happy with making a final ride in his first world cup and riding a very solid qualifying effort.
That was the same time Jesse Sergent did in his first international ride five years ago.
"Dylan is a great kid with big future."
Olympic omnium gold medallist Lasse Norman Hansen (Denmark) gained the gold medal in 4min 20.875sec with a comfortable win over Ireland's Martyn Irvine.
Kennett, BikeNZ's only rider at the World Cup, returns home later in the week before heading to Adelaide for the Oceania track championships starting on November 28.