You only need 4 eligible flights. These are any flights operated by BA (i.e. BA metal), any flights marketed by BA (i.e.. BA flight #), or flights operated AND marketed by IB.

If you each have 390TPs, and providing that your review date is April 8, you should achieve Gold. You will achieve silver as soon as you reach 600TPs (in CW probably by the time you're in HKG. Then, as soon as you reach 1500TPs you'll get Gold, and keep it until your next review date (the one in 2014), with a soft landing to Silver for the year after that. As soon as you have reached either tier (meaning as soon as the points are posted) you will be able to use the privileges of that tier.

Seeing as you are flying EDI(?)-LON-MCT (2 flights) and also MIA-LON-EDI on BA, you will have your necessary eligible flights. Presumably your flights to PHX were on BA metal, meaning that after your flight to LON you will have your necessary eligible flights.