Your FILs current clinic should have a "transient coordinator" which is often the social worker. (A traveling dialysis patient is usually referred to as a transient.) That person should be able to help him set up travel arrangements, and should be able to help him find a clinic in the Orlando area. I would recommend to start the ball rolling now. June, and all the summer months actually, are usually quite busy. The dialysis clinic I work at is often full during the summer with transients. Those that wait too late to set up arrangements have to be turned away.
If he currently runs at one of the "big chain" units (Fresenius, Gambro, Davita, etc) it's often easier to "visit" another clinic within the same chain. They have access to his insurance info, run sheets, medical history, etc., in their computer system.
As far as transportation, I doubt the social worker at his current clinic can help much, as they probably don't know the transport companies in Orlando. The social worker at the facility he will be visiting MIGHT be able to help with transportation, but you might have to pay out of pocket. Transportation is usually covered by Medicaid (not Medicare) and Medicaid is only good in your state.
Hope this helps.