If you register between now and 19th April 2019 you will earn double Avios on your next 6 individual British Airways flights, including those operated by Comair in South Africa. Transatlantic BA-codeshared flights which are sold by BA even if operated by a different partner are eligible (i.e. your reservation has a BA flight number), but unfortunately non-transatlantic BA codeshared flights are excluded, e.g. those to Japan.
If you do manage to get all 6 bonus Avios flights you will be credited with a further 2019 Avios. You must use this link to register.
Note that by ‘flight', this actually means individual sectors, so if you are flying London — New York — Los Angeles round trip, this counts as 4 out of your maximum 6 sectors. Presumably if you are flying London – Australia which is all on a single flight number this will credit as one sector, in the same way that Tier Points are calculated this way too.
If you are unsure how many Avios you will receive I suggest you use the official Tier Points and Avios calculator to and see how many Avios you receive before cabin and status bonuses are included.
Important thing to note is that flights can only be eligible if it is booked AFTER you have made your registration, which means that any existing bookings will not count towards the bonus.
If you have a bunch of short haul flights coming up followed by long haul flights then it actually makes sense to register as late as possible in order to get the double Avios onto the longer flights. As stated the latest you can possibly register is 19th April 2019, but you can travel right up until 31st December 2019. Here is the link to register once again.