The 33-year-old from the Leeswood, near Mold, died following a collision on a roundabout on the A541 Chester Road in the town.
His family have described him as a talented furniture maker "tragically taken from us at a young age".
A 45-year-old Ford Fiesta car driver was arrested after failing a drugs test, and has been released on bail.
In a statement issued through North Wales Police, Mr Bennison's family said "life will never be the same without him".
They said he was an incredibly proud and loving father to baby son, Osian. They said he had described him as "his greatest achievement and the best thing that ever happened to him".
Police are continuing to appeal for witnesses to the incident, which happened just before 10:00 BST on Monday.
A motorcyclist killed in a crash in Flintshire on Monday has been named as Lee Bennison,