This is an old project but a new posting here.
My spouse found a picture of a chair like this about 25 years ago. I extrapolated the dimensions from the picture and because I could not see how the seat hooked to the rails I developed my own design. I reinforced the wood hooks with a metal plate to prevent any breaking of the end grain. (see picture 2) They are all made from oak with an oil and wax finish so they could be easily refinished with some steel wool and more oil/wax finish.
We have not seen any chairs like this since she clipped the picture from a magazine. I have searched the internet without results. I have made about 18 for family and friends. The children seem to enjoy using them until they were about 12 years old and they stood up well to some hard use. The last of my grandkids stopped using theirs last year.
Plans are posted but I do not know if this design has a copy write so don't try to make any for sale without checking.