It seems to be knit sideways in alternate stockinette and reverse stockinette rows to look like ribbing. The long points are cast on at the end of a row, knit and then cast off. It'll take some experimenting to get just the right shape but it's do-able.
Lionbrand yarns did a series of flower patterns and you may be able to find some that you like on their site by searching for knit flowers. A link to my search didn't work but here are some examples:
Please do post a photo when you finish and have fun knitting this one.