Little flower, little flower?

I am finishing up a baby cap. The picture is on page 3 of the “Little Sublime hand kint book” (600?). On the front of the book is a picture of a baby girl in a white sweater with pink edging. The hat has a flower adornment on it and the instructions (page 11 FLOWER) are these:
First: cast on one stitch, slip stitch onto left needle
First row: cast on 7 stitches
second row: cast OFF 7 stitches, slip remaining stitch onto left needle DO NOT TURN!
Repeat 1st and 2nd row 13 times
fasten off the remaining stitches.
To finish: Join back seam (of cap) Sew on button (under chin) and run thread through straight edge of flower piece, pull tightly and secure. Attach flower to bonnet.

I cast on with thumb and fingers.
I cast off with needles as if doing a decrease on an edge
I don’t know how to do "Don’t turn"
I end up with a string (chain) of little hanging rows the linking yarn seems to stretch at will but will not be drawn up so that the little hanging things are closer together.

I think I am doing the “don’t turn” piece wrong, but I don’t see what difference it makes given that I cast on to the right needle anyway?
How does this “draw up”?

All and every suggestion will be most welcome!
Thank you,

Don’t turn just means, don’t turn your work like you normally do at the end of a row. Instead, with that one st that’s left, CO more sts, and repeat row 1 and 2 again. What I would do however, is to turn and use the Knit co instead of the the thumb cast on, then you’re ready to just BO the sts. You’re supposed to end up with a chain of stitches, you join them to make the flower at the end.

Do you have a video of “knit cast on”?

Woops! I found a good video out there in the great ether!

Thank you again Suzeeq–your suggestion is working.

There’s actually one on this site, along with many other ‘how to’ videos.