Does anyone know who specializes in making transmission oil lines for an 1989 Buick Regal Custom 2 door?

GM used numerous styles and shapes and changed types often. The wrecking yard is a good place to see many of them and pick parts to use or duplicate. low cost that way. If you seek to duplicate them with new materials, take the cheap used ones to a hydraulic line repair business. If they make hoses for farm, heavy equipment, automotive, etc. You can bet they have it, make it, or order it and assemble it. Try the phonebook or the equivalent as it applies to where you are.

After you determine the fitting entering the trans, and the fitting entering the coolertank, they can make anything to length. Try to reduce the length of the flexible line to a minimum. Or buy in bulk and make your own but the benders prices add up. they have them automotive or at a plumbing supply. reduce the number of connections and try to eliminate quick connect fittings. unless you have a pit crew,and a sponsor, you do not want those.

What type of place would do this line of work? Can I go to a transmission specialist for the lines too be made?

Specialist in hydraulics and supplies. they supply parts and equipment. You ask at your NAPA and get directed to the shop for repairing hydraulic lines. light or heavy equipment hoses, solvent tanks, all the things that deal with all fluds hydraulic. or the phone book. I just ask at the parts store and go from there for my area.