I purchased Channels for Apple TV. Now I am using Fire tv

Can I download the Fire TV version for free?

You can download the Channels DVR app for free, but you must have a connection to a Channels DVR server to use it. For live TV viewing only, you must purchase a new copy of Channels for your new platform. (And if you want Channels for your non-FireOS Android phone, tablet or other device, you must also purchase a copy of Channels.)

Purchases from one app store are not transferable to another.