A new kind of oscillator circuits is now introduced on the electronics market: LC on chip oscillators able to beat quartz oscillators.
http://www.eetimes.com/electronics-news/4209970/CMOS-oscillator-said-to-beat-quartz
If we look at the circuitry (http://www.eetimes.com/ContentEETimes/101022_rcj_idt1.jpg), we see an integrated coil which is equivalent to a flat bifilar coil whose the two wires would be connected in series, resulting in only one. When we follow the "winding", we understand that each half left or right section lies near another one in such a way to maximize the self-capacity of the coil.
This can be a model to design our flat bifilar coils with the two wires in the same plane.