Currently, the only way to have FrostWire Plus (the fully featured FrostWire version from frostwire.com) ad-free is installing FrostWire Basic from Google Play first, then paying for ad-free subscription via Google Play and then upgrading to FrostWire Plus from frostwire.com.
Because Google Play is the administrator of the subscription, the information is attached a specific Google Play Account, not the app itself. If you switch devices but log in with the same Google Account or uninstall and install the app again, the ad-free subscription should remain active. Sometimes you just have to restart the phone for Google Play Services to update the settings for the apps on your device.
If you already paid for Ad-Free on FrostWire Basic, you can install FrostWire Plus in order to have more search results. Remember that users who have not paid will see ads on FrostWire Plus.