Answer: Improper Materials, Improper Configuration, Unsafe Condition
This kitchen exhaust vent has taken a very long and complicated journey to the outdoors. The homeowner and proud installer had actually boasted that, "Venting this newly purchased kitchen exhaust fan was such a simple process. All that was necessary was to run the vent material across the cabinets and out the existing vent!" The homeowner certainly worked hard on the project, but (besides being pretty unattractive) there are a few concerns.
The venting product used is classified as corrugated flexible venting material and is not designed for venting kitchen exhaust fans. (You may recognize it because it is more commonly used for dryer vents). The material, as it is currently positioned, will trap grease and moisture and is a potential fire hazard as well. Lastly, the vent at the exterior is a plastic dryer vent, also not designed for high temperatures and is a potentially unsafe material for this application.
The current or new homeowner needs to have either a recirculating vent system installed over the stove, or an external vent configuration composed of vertical hard piping rising up to and through the roof exterior.