Edit: Moved this post over from the Tile Scaling for Fire HD10 - #15 post so it’s in a better place for other people to reference.
Sometimes your local news site will provide a radar (similar to how you can use their forecasts).
Based on a search and some quick tests, I believe the Weather Underground ones can be embedded with a refresh interval specified. You can either use the US level map or you can select a region from the drop down and use the Image Link on the resulting page.
https://www.wunderground.com/weather-radar/united-states/animated
You can even drill in a bit further than that to your local region / metro area and then use the ‘Save Image’ button on the page to get a valid URL.