The name 'flame stitch' refers to the flame-like design of Florentine work.
GVE
Hungarian Point
Example of a pattern for Florentine work
http://www.stitchstitch.info/a/florentijns/noorderlicht.jpg
in Italy, the flame stitch is known as Punto unghero (‘Hungarian Point’), suggesting that this particular embroidery style was regarded as originating from Hungary. However, in English the term ‘Hungarian Point’ generally refers to a diamond-shaped stitch also called the Hungarian point stitch.
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Embroidery stitches