If you purchased the app and you'd like to install it on another device with the same operating system, you can do so for free.
If you use the same account on those devices, just make sure to search for the app in App Store / Google Play and install it for free.
If you use different accounts on your devices, you can install the app for free through Family Sharing (iOS) or Google Play Family Library (Android).
If you have two or more devices with different operating systems (Android, iOS, macOS), it is necessary to purchase the app for each operating system.