It sounds like either the chain or freewheel are worn, possibly both. Are they original? Uniglide freewheels were not designed for index shifting IIRC, and the 6-speed derailleur may not have been either.
Indexing derailleurs have a "floating" top pulley that adjusts for slight misalignments, If your derailleur doesn't have this feature the indexing will be nearly impossible to adjust reliably.