You can follow Mclyman's book for general transformer design. They are classic books for transformer design. It shows step by step process for design.

1. Mclyman CWT (1999) Magnetic core selection for transformers and inductors a user’s guide to practice and specification, 2nd edn. Taylor & Francis Group.

2. Mclyman CWMT (2004) Transformer and inductor design handbook, 3rd edn. Marcel Dekker, Inc

The following article also provides good information:

1. J. C. Fothergill, P. W. Devine and P. W. Lefley, "A novel prototype design for a transformer for high voltage, high frequency, high power use," in IEEE Transactions on Power Delivery, vol. 16, no. 1, pp. 89-98, Jan. 2001, doi: 10.1109/61.905601.

2. Rahman, S., Candan, M.Y., Tamyurek, B. et al. Design and implementation of a 10 kV/10 kW high-frequency center-tapped transformer. Electr Eng 104, 2603–2619 (2022). https://doi.org/10.1007/s00202-022-01499-3

You can also follow the equations and steps of chapter 6 of this thesis paper.

Design, Analysis, and Simulation of an Isolated High Voltage DC Power Supply Based on Modular Converter and Cockcroft-Walton Voltage Multiplier Topology

Link: Thesis Design, Analysis, and Simulation of an Isolated High Voltage...