How can I kill weeds between rocks around pool without chemicals?

Vinegar!

Yup, plain vinegar.

My favorite for that is plain old white vinegar. Boiling water will work well too. Epsom salt followed by boiling water also works.

Hello!

There are many natural household type of ways to eliminate your weeds, these very helpful links from Hometalk are a great a great synopsis.

https://www.hometalk.com/diy/outdoor/pest-repeller/diy-weed-killer-38537988?

https://www.hometalk.com/diy/outdoor/pest-repeller/s-9-natural-weed-killers-that-will-save-your-summer-garden-17001086?

https://www.hometalk.com/diy/outdoor/pest-repeller/natural-weed-killer-20665086?

Salt. I sprinkle salt every year on my walkway.

White vinegar. It's cheap and safe.

Yep, white vinegar will do the trick!