Derek, KLIA is a nice and easy-going airport.
I recommend you to call BA in advance or better drop by any office of them, and show your connecting ticket, so they may add as “passive segment” as it is called, your connecting flight to your booking. That will help you a lot at the time of going to the airport. And since both are oneworld, it should work well.
Regarding the MH Golden Lounge, they will grant you access to the right side, the Premium one, only if you are Emerald on oneworld.
I have transited several times KL flying Business on MH. While I was Gold on QR (Saphire on oneworld) they invited me to the left side, the Business Class lounge. But as soon as I became Platinum on QR and so Emerald, now every time I transit there (in my case always flying J on MH), they invite me to the right side which is very nice, comfy, quiet and relaxing. And the staff there are extremely nice and polite.
As it was said above, your flight to BKK will depart from the Main Terminal so u have to take the Aerotrain.
Have a good trip!