On October 8, University of Kentucky announced that students who live on or come to campus will be required to receive a flu vaccination by Nov. 1. The University does recognize both religious and medical exemptions.

To exercise a religious exemption, a student should send an e-mail to ReligiousExemptions@UKY.edu. This e-mail must come from the student and not the parents unless the student is under the age of 18. The email must state that getting the flu shot will substantially burden the student's free exercise of religion. We recommend keeping this statement simple and there is no need to include details. There is no form or notarization required.
 
For a medical exemption, a student must register with the Disability Resource Center. The Center can be contacted at DRC@UKY.edu, and more information is available here.

KY Constitutional Attorney, Chris Wiest stated the following.

​"The next battle and uproar, I expect will be on forced vaccination. No, there is no vaccine now. It is in phase III testing. Best guess is early 2021.
But Kentucky law does permit forced vaccination. KRS 214.036:

“Provided, however, that in the event of an epidemic in a given area, the Cabinet for Health and Family Services may, by emergency regulation, require the immunization of all persons within the area of epidemic, against the disease responsible for such epidemic.”

https://apps.legislature.ky.gov/law/statutes/statute.aspx?id=8778

Proponents argue it is necessary to protect community health. Those opposed see it as a matter of fundamental liberty and autonomy.
On a federal level, it’s highly likely to be constitutional under Jacobson v. Massachusetts.

On a state level, I wouldn’t hold my breath on this, considering we sort of litigated the issue, on the chicken pox vaccine, up to the Kentucky Supreme Court, and lost, and there were legitimate religious objections in that case that implicated Kentucky’s RFRA. And still forced vaccination okay.

If it’s something you don’t want to happen, it’s in the hands of your state legislators. If it’s something you care about, you should ask your legislators where they stand on this issue and if you are opposed ask them to repeal this and prohibit forced vaccinations. And then vote accordingly."