There's not an easy way of doing this that maintains easy interchangeability with your existing wheel and freewheel.
Bicycles with thru-axles didn't exist in the 80s. You have a quick release or nutted axle. Your first challenge will be to determine what the frame spacing on your bike is, and then put the correct endcaps on the trainer to match it.
Old 6-speed freewheels didn't have standardized cog to cog spacings. New ones do, but there are no off-the-shelf cassettes that match it. So in other words, there is nothing you can put on that will "just work" with your existing setup.
You could put a 7-speed cassette on the trainer, plus a 4.5mm cassette spacer, plus the 1.85mm spacer that your trainer probably came with. The chain will need to be a 7/8-speed. The cassette's total width (distance between the plane of the big and small cog) will be be close to that of your 6-speed freewheel. Thus, with this setup you would likely be able to adjust the rear derailleur to work correctly with the cassette. You will have to choose one whose large cog doesn't exceed what the derailleur can handle. Get one with a 28t if you want to be safe and avoid having to figure that out.
You could get a 7-speed cassette where the first six cogs would be satisfactory for the trainer, grind out the rivets that hold it together, discard its big cog and existing spacers, and then add spacers that make it duplicate the exact cog-to-cog spacing of whatever freewheel you have. The spacers would have to be exact, so this would likely take a long time and be expensive. But, it is the only route to get something that matches what you have in terms of drop-in interchangeability.