When I try to download the iOS 10 beta it brings me to the iOS 9 beta which I downloaded in the past
How do I reroll my device to get iOS 10?
Have you got the developer profile on the iPhone? it will then install the delta OTA update to iOS10 via the normal Setings > general > software update method.
get the "iOS10 Beta Configuration Profile" from here https://developer.apple.com/download/