Take 5 of
these to get a 0.4 mm thick PCB.
0.4 mm ferrite should not be any problem but its function will be almost none and would very easily be broken if mounted non flexible, at a thin/flexible PCB.
Max current is depending on what losses and temperature rise you can accept, amount of mechanical stress and aging effects.
Is this enough thin circuits/PCB?
View attachment 71920
And it is a even smaller circuit inside these three boxes.
Inside one of them:
View attachment 71921
This circuit was designed 40 years ago (1972), 10 years after the first commercial two-transistor IC.