This is a wonderful looking stitch. Each loop drops vertically from the stitch line, instead of lying on it. The way the loop is twisted gives it a knotted effect and a complicated look. Ideally, it follows a right to left direction.

You need to be aware of the twisted chain stitch to be able to do rosette chain stitch. I will follow a curved and spiral stitch line to demonstrate this stitch.
rossette stitch 1   rossette stitch 2
Fig 1: Bring the needle out through a point A which lies on the stitch line. Put the needle in through B which lies on the left of A.Note that B lies on the stitch line too. Bring the needle out through C and loop the thread around the needle as shown.   Fig 2: Pull out the needle to get the twisted chain. Now take in the needle through the right ‘leg’ of the twisted chain as shown. Do not pluck the fabric underneath.

rossette stitch 3   rossette stitch 4
Fig 3: Once the thread is pulled out, we get a knotted lookign loop like this.   Fig 4: For the next loop, put in the needle on the stitch line towards the left of the existing loop and wrap the thread around.

rossette stitch 5       rossette stitch 6
Fig 5: To give the knotted effect, take the needle in under the right ‘leg’ of this newly made loop.   Fig 6: Continue this procedure to finish the entire pattern. Observe how the chains or loops close in and open up at various curves.