If you are going to wind a transformer you will need to have a layer of insulating kapton sheet covering each completed layer of winding, along with a gap at the ends so that it will not flash over. Typically you will wind for 50-100V per layer, so to get to the 1kv centre tapped one you want that will be between 20 to 40 layers of windings with kapton tape cover. Needs a big core, and as the primary will be wound below it the leadouts will need to be insulated for 2kV fro them as well, along with at least 5 layers of Kapton tape as winding separator between primary and secondary. If you really need equal capacitance windings then you will need to split the windings so each half is wound at the same time on just under half the core width, with a spacer tape applied to each layer to keep the tape layer flat. Those are a PITA to wind, I have done some for other voltages that are lower, and they take a day or more to get done properly, as you are going slow and with 2 spools with a lot of stopping for tape and tie down..