Not sure about style, not sure that it matters as flat horns were made by many different people in not only North America but Europe and other places and in many different shapes.
Start by getting your horn to the desired thickness as you would any horn, well tapered. Once you are satisfied with the shape and thickness, remember you will be scraping it more after pressing, press it flat. Once dry scrape it to the shape you want.
Here is the press I use. The thickness of the wedges determine the final interior thickness. Once you start pressing the horn the center one goes in first, it is an Isosceles triangle, the others are Right, the outer ones have the edges rounded to shape the horn sides. Flatten, insert wedge, continue to press and add wedges, if you have more space than triangles tap some smaller wedges in between.
Hope this helps.
Tim C.
