Can any of the flyback controllers be used for Hv applications (Output voltage of 12kV, 1mA)?
That is all about transformer design. If the chip has a pin called FB ( feedback) it is usually around 1.25V and is fed information from a voltage divider, which can just as easily divide 12000 as 12
Usually these things are done with a lower voltage transformer and a string of diodes configured as a voltage multiplier.
In fact IIRC there is a company VMI ( voltage multiplier INc) that sells these stacks of diodes.
The diode is also a problem as it needs to be a 20kV rated piece
The controller is not your problem the rest of it is