As a general rule bathroom fans are not suitable for use in the kitchen as many have no filter inside them.
Can you use bathroom fan in kitchen.
Bathroom and kitchen exhaust fans also can transmit large volumes of moist humid air into the attic or other confined spaces.
This would be the minimum ventilation.
Fans installed above kitchen ranges must be listed for that application by ul and must be designed to handle grease and high temperatures.
Have seen many bathroom fans used in kitchen over the years and all eventually fail in the same way in that oil grease in the air from cooking vapours etc build up on the fan blades and inside the fan casing causing the fan motor to sieze and stop working.
You cannot by code and should not by practical reasoning share exhaust venting between a kitchen exhaust and a bathroom exhaust fan.
An alternate approach is to use a ducted range hood or downdraft exhaust and a bathroom ventilation fan to exhaust the general odors and moisture in the kitchen.
So if you have an 8 foot x 10 foot bathroom you would need at least an 80 cfm fan.
You say the kitchen is 120 sf but you need to take in to account the height.
That would be 960 cf assuming 8 ft ceilings.
A bath fan just won t cut it.
This can lead to wood rot mold and mildew.