To get benefits you have to file a formal claim with the Kentucky Department of Workers Claims and get an Administrative Law Judge to order the Fund to pay you. You can file for benefits on your own, but you must prepare technical documents, file evidence, attend depositions, and argue the right points of law before an administrative law judge. You will probably need an attorney to get through the claims process and get benefits. Most attorneys will handle these cases on a contingency fee, so you do no not have to pay them until they win your case.
I discuss some of the issues in filing a claim against the Uninsured Employers Fund, contingency and claims process in my FAQ section: