Hi Mallie ,
How long it takes depends on how long you stop for lunch !!
Seriously , Messongi to Kassiopi will take around 1 hour .
From Ag . Gordis head out of the resort on the mountain road [ turn right instead of left for Corfu town ] .......head through the mountains to Ag . Matheos . From there you will drop down to the main N-S trunk road and be only 2-3 km's from Messongi .
The trip through the mountain villages is spectacular and not to be missed for the scenery and way of life that the locals live . [ budget an hour for that part of the trip ]