I am interested in the PLATINUM CHALLENGE, how do I go about this?

Do a search on this board and on the AA board (look at the sticky at the top first). It has all the info on how far you have to fly within 90 days of signing up to qualify, and in what BA classes you can do it. One long haul should do it.

The best time to sign up is from June 15th, I seem to remember, as that gives you Sapphire status from the day you complete the challenge until the end of the following year. Do it earlier in the year and you only get status for the rest of the current year. But the AA board (and old threads here) have tons more information.

The miles for your qualifying long-haul flight will, of course, be credited to an AA account and not your BA Miles account. However, you can use these miles for BA flights and you can buy additional AA miles, transfer hotel miles or get the UK AA Visa card to top up your mileage to enough for an award. AA redemption levels are lower than BA anyway, even for flights on BA metal!

After your first flight, it is up to you whether you go back to using your BAEC account to get mileage (and just flashing your AA card for lounge access) or continue to accrue on AA.