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You can then post your questions, I may be able to answer them.
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Read carefully page 2 of the document SEM100 DRA4. Based on the RMS currents of the windings you calculate the required wire size.
It should be noted that for switching power supply transformers, the current density is not really that important. What's important is the power dissipation. so you can have current densities much higher than 4.5A/mm2 (much thinner wire) if the power dissipation is low.
To keep losses low, you need to know that the skin effect will force you to use thinner wire. You need to do a few iterations until you get the best wire size. Thinner wire is better, since the skin effect has less influence. And although it seems that the thinner wire is not capable of carrying too much current, the actual dissipation (and temperature rise) will be lower.
The process of designing a good switching transformer is relatively complicated, but not impossible to learn.
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