Qantas FFP allows free transfer of points(miles) between eligible family members. But QF ffp is in general poor value.
With US Airways you can get miles for flights 6 months before joining the US ffp
http://www.usairways.com/en-US/divid...mberguide.html
Transferring awards
You can use your miles to book an award ticket for someone else. Just provide the passenger name(s) when you make the reservation.
You can transfer your miles in 1,000-mile increments to another member's account for $.01 per mile and a $30 processing fee through our buy, share or gift miles program (see link below).
BA will be best
Your parents can get an award flight for you. It is not unusual for 1 family member to manage the ff accounts of other family members
http://www.flyertalk.com/forum/onewo...help-here.html