I answered your question with more questions in the thread you posted on the San Francisco forum. This is probably not something you need to do.
With regard to the location questions: (1) No, BART does not stop at Jack London Square, and (2) no, it is not an enjoyable walk with luggage.
The Amtrak station is not in the very center of Jack London Square, so while most people will direct you to the 12th Street/Oakland City Center BART Station, it's actually faster to use the Lake Merritt BART Station if you are walking. The walk is okay during the day, but one has to pass under the freeway, which can be a bit unnerving during the later evening hours.
I recommend catching the bus instead of walking. The bus can be caught at the 12th Street station. Take AC Transit Route 72 or 72M, both of which terminate right at the Amtrak station. (Be sure to take the bus going the correct direction.) More information: http://www.actransit.org