Butterick Hat and Scarf Pattern, # 5218, May 1924 Delineator
The vintage cloche hats I’ve seen have usually been either felt or straw, and store-bought. A milliner needs a hat block to pull a felt shape into a cloche, and stitching bands of straw braid into a hat requires great skill (and a specialized sewing machine, unless you do it by hand.) But that did not prevent women from making their own cloche hats from commercial patterns.
Make a Replica Gored Cloche Hat on a Sewing Machine
Two more views of Butterick Hat and Scarf # 5218, May 1924
Butterick sold several kinds of gored cloche hat patterns in the 1920s. The pattern for this one, # 5218 Hat and Scarf, first appeared in May, 1924, and continued to be shown in illustrations in The Delineator magazine for a year, so it was in style through 1925. This hat is for “Ladies and Misses, ” i.e., adults and teens. (None of the magazine descriptions says whether this hat has four, five, or six gores. It looks like four or five with a center front seam to me.) In the winter, woolen fabrics were recommended for the hat and matching scarf; in summer, silk was suggested. 
This simple hat could be ornamented in many ways.
You could make it in plaid or solid-colored fabric:
The hat and scarf could both be embroidered to match:
You could embroider just the turned-back brim:
You could embroider the crown: 
You could weave together an easy rectangle of grosgrain ribbons, with diagonally trimmed ends hanging free:
The ribbon trim could match the hat color, or contrast with it:
You could use contrasting ribbon trim on the hat and embroider your monogram on the scarf in the same color as the ribbon:
Or you could add purchased trim: a flower in summer, a pom-pom of silk-covered cording or feathers, a ribbon cockade, etc.
Sample purchased trims, not shown on hat #5218
You should be able to adapt a modern four or six gore hat pattern for your cloche; of course, wool or silk will need interfacing to be stiff enough. Milliner Wayne Wichern uses tailor’s hair cloth as interfacing on his custom hats. If you match the grain of the fabric and interfacing carefully, you can use steam and a press cloth to shape the hat around a tailor’s ham. Unlike synthetic interfacing materials, real haircloth, like silk and wool, is an animal fiber and responds to shaping with moist heat (Fusible interfacing is not recommended! A cloche needs to stretch.) For inspiration, visit his website. Wayne Wichern Millinery. He is very creative about creating lovely trims from scraps of felt and straw! And he offers classes at his studio in the San Francisco Bay Area, in case you’d like to take a vacation and come home with a hat.
Hats and trims by Wayne Wichern, Milliner, photographed at his lecture at the De Young Museum
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