Installation on Linux not really documented (have to dig though the GitHub wiki, nothing is documented regarding GnuPG integration on their website).
Once GnuPG integration works, it pretends it cannot find the public key for a recipient (manual searching the key on keys.openpgp.org works flawlessly). If you somehow make it work, it basically replaces the editor of your webmailer with this plaintext editor (so you can't really use the default editor of your webmailer anymore).

All in all I can't really recommend this extension.
Either you trust your webmailer enough to give it your keys or just use a local mail client.

If you still want to bother trying this extension, for Linux Mint/Ubuntu you can enable GnuPG integration like this:

1. install gpgme-json (it prentends to automatically set up the firefox native-messaging-hosts file for you, but that's a lie)
2. create the "native-messaging-hosts" config "/usr/lib/mozilla/native-messaging-hosts/gpgmejson.json" with the following contents

{
"name": "gpgmejson",
"description": "Integration with GnuPG",
"path": "/usr/bin/gpgme-json",
"type": "stdio",
"allowed_extensions": [
"jid1-AQqSMBYb0a8ADg@jetpack"
]
}

3. restart firefox
4. mailvelope should now detect your GnuPG backend