One thing you should be aware of is that you might like these strings BECAUSE they're old.
If these are GHS Brite Flats they aren't really flats at all but roundwounds that are ground down to "half rounds". The name is very misleading. But many roundwounds can benefit from a break-in period too, particularly if you happen to like a warm, mellow tone.
If you install a new set of GHS Brite Flats you might find that you don't like them at all. Or at least not nearly as much as that old, rusty set. Give them some time.
The GHS Brite Flats seem to be almost universally disliked but I suspect a lot of people never got past the sticky "new string" phase, which is particularly bad with these strings. They're also stiffer than standard roundwounds of similar gauges, which may not be to everyone's taste. But they were also the stock strings on Stingrays back in the day. I suspect a lot of people hating these strings will actually love the TONE of these strings on countless classic recordings. Tonally they have that kinda "dry" 70s vibe to them. Depending on personal taste I guess the tone can be described as either "mellow" or "dead".
If you don't mind the rust/dirt the best thing you can do is probably to keep playing the old strings for as long as possible. Or be prepared for a frustrating break-in period.
FWIW I didn't like the GHS Brite Flats much myself. They were too dead/lifeless and stiff for my taste (and I generally like mellow sounding strings). But they're certainly unique strings and if they work for you: GREAT! I applaud anyone who use their ears and find their own personal tone/style.