There are a wide variety of scenarios regarding aboveground storage tanks (ASTs). Below are several resource that can narrow your search to the scenario that fits your situation the best. ASTs storing volatile organic compounds may require an air permit or registration from the KY Division for Air Quality depending on the material and potential emissions calculated for the type of tank, material and usage. The EPA provides free software to put in all the variables and come up with a potential to emit (PTE). See: https://www.epa.gov/air-emissions-factors-and-quantification/ap-42-chapter-7-tanks-software-frequent-questions
The At-a-Glance document covers the most commonly issued environmental permits and authorizations issued by the Kentucky Department for Environmental Protection. It also lists the PTE thresholds that trigger the need for an air permit in Kentucky (outside Jefferson Co). The Common Permits document lists commonly issued industrial environmental permits, application fees, and their regulator timeframes.
A facility that handles pesticides, hazardous or solid wastes, bulk quantities of raw material and other potentially polluting substances should develop a Groundwater Protection Plan (GPP). GPPs are to be implemented upon development and are not dependent on approval. See https://eec.ky.gov/Environmental-Protection/Water/GW/Pages/GWGPP.aspx
Agricultural operations also have control requirements for petroleum storage: https://eec.ky.gov/Natural-Resources/Conservation/Documents/On-Farm%20Petroleum%20Storage%20and%20Handling.pdf
For actual or threatened releases of any pollutant see: https://eec.ky.gov/Environmental-Protection/Waste/Pages/EmergencyResponseBranch.aspx
Other resources:
The Kentucky State Fire Marshall - Hazardous Materials Section is responsible for the permitting of flammable, combustible, and hazardous material storage vessel installations. They issue permits and plan reviews of installation, repairs, and modifications on underground storage tanks (UGST) and aboveground storage tanks(AGST) and related components. Additionally, the section regulates the sale and storage of Liquefied Petroleum Gas (LP). The following link will provide direct contact information for the office of the Kentucky State Fire Marshall; https://ksfm.ky.gov/new_docs.aspx?cat=70&menuid=76
Certain petroleum storage units may be subject to the federal Spill Prevention, Containment, and Control (SPCC) rules as well. An applicability flow chart is available at this web page.
https://www.epa.gov/oil-spills-prevention-and-preparedness-regulations