If you collect the seeds, they will need to be nicked or roughed up, and then soaked for a day before starting. 18°-20°C heat. Mine was started in the spring.

I don't know the answer but I wish I had one in my garden, lucky you

Grandad. I have another one in a pot :o)).
The one I have in the ground is as big as it gets, they are best grown against a wall, thats what I read but if one has room like I have I think it looks better where I have it, it is outside near my kitchen, I can also see it from our lounge area & when the sun shines on it, it Glows & Brightens up our garden :o)) xx

Sophora Sun King is a grafted plant, meaning it has a different rootstock from the upper parts. Not sure how well any seedlings you manage to grow will do - probably won't be so vigorous or something but that's no reason not to try. I read elsewhere that soft or hard cuttings are very difficult to get growing, but you could try soft cuttings around May time from unflowered shoots. Otherwise, propagation is by grafting onto a suitable rootstock , see link below, under propagation

https://www.rhs.org.uk/plants/125089/Sophora-Sun-King-Hilsop-(PBR)/Details