In this circumstance the light kit could be connected to a dimmer switch and the fan motor connected to a toggle switch.
Can you put a ceiling fan on a dimmer switch.
You can install a ceiling fan light dual dimmer switch to operate the fan speed and light intensity from the original wall switch location.
A dimmer switch as the name suggests lets you control the intensity of the light produced from the light to which it is connected such as a ceiling fan with a built in lighting fixture.
A broken ceiling fan motor and a house fire are obviously not ideal outcomes however there is some good news.
The wall dimmer switch reduces power flow and interferes with the fan control.
You may need an electrician for this.
The new switch does require an additional electrical wire.
Replace the wall dimmer switch with an on off switch.
By all means you can connect a ceiling fan directly to a dimmer switch but you may run into problems along the way.