We know of no certain grade point average that one must carry in order to be able to have auto insurance in Kentucky. Kentucky does have a form of the No Pass, No Drive law though that authorizes the KY Transportation Cabinet to have administration regulations regarding a minor driver licensing applicant.
This administration regulation, KRS 186.400, requires participating schools to notify the Transportation Cabinet if a minor withdraws from school or is academically deficient. Thus as a 16 or 17 year old and you drop out of a participating public school or are deemed to be academically deficient, you will lose your driver's license.
The No Pass, No Drive only states a student to be found academically deficient but did not go into detail of how that is determined. To find out information what grade point average might deem you to be deficient in this way, contact the Kentucky Transportation Cabinet.
If you lose your license due to this state regulation, it could be difficult to an auto insurance company to cover you. On the flip side, some insurance companies offer discounts for students with good grades. This good student discount is generally available to students (under 25) who have a grade point average of a B or higher.