You haven't mentioned ammonia, that is important. If it's not zero, that will be harming the fish.
It is very unusual to have zero KH (alkalinity) but GH of 250. They are usually high or low together. How are you testing, strips or liquid testers?
Of the things you have tested:
Nitrite is zero, which is good.
Nitrate is high, it needs to be under 20 ppm. If your tap nitrate is zero, either it's an inaccurate test or it's being made in the tank. With low tap nitrate, water changes should reduce the tank level then you need to stop it getting high again. Your water quality report on your water company's website should contain nitrate which will confirm or otherwise your nitrate tester.
Alkalinity/KH is not really important. All it does is stabilise pH. If it really is zero, it means your pH is likely to fall over a few days.
pH 6.5 - this suggests soft water, which conflicts with your hardness reading. Again, look on your water company's website for hardness - it won't be in the table of your water quality report but it should be available from the same page.
GH/hardness - 250 ppm is very hard, which conflicts with your KH and pH.
If you can't find your hardness or water quality report on your water company's website, tell us and we'll see if we can find them.
How long have you had the platies and did you get them all at the same time? If you did, it could have been an unhealthy batch.
Or there could be ammonia in the water, and if there is, and the hardness tester is wrong and you have soft water, that would make platies more susceptible to ammonia and/or illness.
Edited for typos