The Oneworld rule relating to lounge access is here:
OneWorld lounge access
The key points are - you are BA Silver and you are travelling on a OneWorld marketed and operated flight. The only limitation to gaining lounge access would be if you were OneWorld Sapphire via American Airlines Platinum status (exception 2), or your flight wasn't operated by a OneWorld airline, e.g. by Alaskan Airlines on a codeshare. So you can (read should be able to) gain access. However, as noted above, the lounge is in a different Terminal than your flight.