Yes you can, only if theres no core leakage will be very high, most of the ingoing power will be lost, but then it depends what the trannys for, that might be acceptable.
Wind the primary and secondary both wires together, or bifilar.
Because the tranny is flat if the secondary has a lot more turns it will end up a long way off the primary, this will much worsen the coupling, it probably wouldnt do much more than light an led.
I'm guessing this is for wireless energy transfer.
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