No, British Airways is not included in the free companion tickets. It is a limited set of airlines that offer these, and in any case, the deal is that you only get a companion ticket if you purchase a fully flexible fare. Amex's definition of the cost of a fully flexible fare may differ from yours. Plenty on this if you search the Amex forum. This does sometimes work out cheaper, but its main advantage is for the businessman getting a ticket for himself on expenses and being able to take his companion for free. (It shows up as a single ticket on the Amex statement).

According to latest literature from Amex, 2 for 1 business class available for Air Canada, ANA, Continental, Delta, Emirates.

Complimentary upgrades likewise only on full fare tickets, on ANA (J to F), Emirates (Y to J, J to F), United (Y to J).

Special fares (whatever those are) on Air New Zealand, AA, ANA, LH. Special companion fares on South African and United.

The useful 241 deal with Amex Plat chargecard is that the £120 annual charge for the top BA Amex credit card is waived, which gives 1.5 miles per £ spent and a 241 (BA miles) voucher after a spend of £10,000 in 12 months. Add to this the Plat Chargecard benefits of the travel insurance + the car insurance + the two Priority Passes + the FHR deals. Depending on your travel pattern, you may or may not consider it worthwhile.