There is no good way to "wrap" onto a non-cylindrical or non-conical surface. There are lots of "bad" ways.
You can use patterns and 3D sketches to get the job done, which is how I would approach it. I can show you an example of how to do it if you can upload the part you have so far.
1. Create the revolved shape.
2. Create a helix, and sweep a flat surface along that helix which interferes with the revolved shape where you want the diamond pattern to be. You only need to do one small iteration, remember you can pattern the rest.
3. Insert>Curve>Split Line to create an edge where the diamond pattern will go.
4. Sweep Cut with the groove profile required. Use the split edge in #3 as the path.
5. Circular Pattern as required.
Here is the model that I have started. Ill try some of your suggestions and see what I can do. Thanks
I have attached my method. It looks like you are on the right track, but when I attemped it, I ran into a few stumbling blocks. So here are some tricks for when you run into issues.
1. I used Surface Sweep to make the twisting shape, I find that easy to control.
2. I could not get the pattern to work. You can try "geometry pattern" sometimes, which uses a different algorythm to solve, however I could not pattern both the clockwise and counter-clockwise this way. What I did was unchecked "merge bodies", which made them separate bodies. Also note that you cannot pattern features this way, so make sure you pattern the bodies. Then I merged the bodies later with the combine tool. This works around some of the geometry errors.
3. I also used the "move face" tool to extend some of the ends.