Wireless power receiver coils can be designed onto flexible printed circuits (FPCs) - do you have a design guide for this?

Coil design is really an art, requiring extensive simulation using complex software.  So there is no design guide that is provided at this time.  If WPC compliance is desired, then utilizing one of the WPC-approved coils would provide the easiest path to Qi certification. If PMA compliance is desired, the easiest way would be to follow  the coil implementation proposed in Appendix B Receiver Implementation (Informative) of PMA Receiver Specification - System Release 1.

Aluminum is possible, but the losses would be greater and the efficiency lower. However, these can be offset to some degree by greater area or coil volume – but then you venture away from a WPC-approved coil design or PMA proposed implementation. So, there are tradeoffs.