Range hoods must be vented using metal duct. Given a choice between flexible metal duct and smooth metal duct, go with the smooth. The ridges found in flexible metal duct create turbulence and will diminish airflow.
NEVER use 4" dryer duct or any plastic duct on a range hood installation. The minimum size duct allowed on most range hoods is 3 ¼" by 10" which is equivalent to 6" round. More powerful hoods require even larger duct sizes up to 10" round. Consult the specifications for the model you have chosen.
When remodeling, changing hoods or cooking equipment types do not reduce the ductwork size to less than the size specified for the range hood. Decreasing the duct size restricts the performance of the range hood ventilator.