I'm not sure about the duct booster or if that is what you want to exhaust excess grease. You really want a grease filter in the hood of the microwave to catch the grease before it gets into the exhaust ducting so you don't have a fire hazard burning your house down and grease exhausted all over the place. Grease will just gum up the motor and fan blades after a while which will then slow the fan down, generate excess heat, and start a fire. Contact your city inspection department to see if that is allowed.
If the exhaust fan in the microwave doesn't move enough air to get the grease up to the grease filter in the microwave, then consult with the microwave company. Contact the company manufacturing the duct booster for their input and if that is an approved use. If you are frying lots of chicken, then maybe you should look into the commercial hoods the restaurants have to use.