The petals of this flower are embroidered exclusively with long and short stitch. The center is made also with long and short stitch but covered with detached buttonhole stitch or needle lace, stem stitch and Turkish work.
Regarding the petals, to guide you in their realization I chose the following method
Below is a photo of all the petals finished with 4 arrows and letters. Each letter corresponds to the color gradient I used for this type of petal. Just look at the photo to see how to embroider the flower.