Absolutely! Now, I don’t read a lot of regency fics really but I certainly know of a lot of popular ones – I’ll split this between fics I’ve read and ones I have not. If I remember anything particularly of note about any of them I’ll jot that down as well.
regency/knight/king fics I’ve read
black knight, white queen – an absolute classic, rey is a ward/heir and kylo is, well, the black knight…
crown & duty – game of thrones mashup, ben is king of seven kingdoms – and rey is his hand
primae noctis – not a king, but a baron. more of a medieval setting and I liked it, but watch the warnings if you have certain sensitivities
kingdom of crystals – more of a fantasy/medieval setting but still fits the bill!
inheritance of the resistance – another classic, we get jealous ben! who is he jealous of? his dad! don’t worry though, it’s not like that.
the desert rose – not quite what you had in mind I suppose, but he is a knight – think arabian nights and harems
sustenance – LISTEN okay so I may have started reading this for the lactation kink, but it is a full fledged victorian/regency AU complete with prodigal son Captain Ben Solo returning to the estate. It’s very very good.
ones I haven’t read
force & force ability – I will give you two guesses what this one is like! and the first one doesn’t count XD
rainfall – described as a jane austen fusion and rey’s last name is darling so I think this probably suits your needs
the beast within – seems interesting, but a darker take so maybe not quite on point
I hope these are a good start for you! =)