XDA forum user Charlie tells us his Fire TV Voice Remote has received a firmware update taking it from version 351 to version 352. Charlie’s Fire TV is one of the few that has received the new 22.214.171.124_user_512073320 firmware update, so it is likely that your Fire TV Voice Remote will not receive this update until your Fire TV updates. It does seem like this remote firmware update is necessary as Charlie reports that, after his Fire TV updated, voice search stopped working until he updated the remote firmware. As always, there is no way to know what changes this firmware update makes. Maybe one day an update will enable the remotes unused accelerometer.
You can check to see if your remote has the update by going to Settings > Controllers > Amazon Fire TV Remotes. If an update is available, you will see a message asking you to press Select to begin installing the update.