These are 2 ways of folding the fabric square, in order to obtain the original Kanzashi flower, and a pleated variation. The red folded petal is the pleated variation, whilst the green is the original. Here we go:
Take a 10 cm square. (can be any size you think you can handle, it also depends on the fabric structure)
Fold in half. Iron. This is the only fold that needs ironing.
Fold in half again, keep fold towards you.
Take the corner and fold it back to you, leaving it a bit aside so you have a pleat at about 2-3 mm from the point.
... the rest of the story is available on my website, http://quibi.ro/how-to-make-a-kanzashi-flower-cum-sa-faci-o-floare-kanzashi/
For the time being, it is only in Romanian language, but the photo's are quite self explanatory. Should the need arise (i.e. you as for it in a comment or something) I will make it in English too.
Have fun crafting!