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.
Can you use bathroom fan in kitchen.
You say the kitchen is 120 sf but you need to take in to account the height.
The trick is to simply exhaust this air from the fans directly to the exterior of your home.
The general rule is 1 cfm per square foot of space with standard 8 foot ceilings.
A bath fan just won t cut it.
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.
Depending on your usage you might consider a slightly larger fan to make sure you have enough power to clear the room.
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.
You cannot by code and should not by practical reasoning share exhaust venting between a kitchen exhaust and a bathroom exhaust fan.
As a general rule bathroom fans are not suitable for use in the kitchen as many have no filter inside them.
That would be 960 cf assuming 8 ft ceilings.