Not really. You can buy AsiaMiles in order to top up your own account at the time of making an award booking. See:
http://www.asiamiles.com/am/1,,83127_83488_eng_,00.html

But you can't simply buy AsiaMiles to give to someone else.

There are lots of propmotions around at the moment though where you could get some thousands of AsiaMiles by, for example, signing up for a credit card. The AsiaMiles site is pretty good - go there for more details.