Create your Shuriken mesh and curve object to follow.
Add a Path Constraint, a Follow Path (Ctrl+P > Follow Path) parent or whatever suits your need.
After the shuriken is correctly following your path, select it as active object, place the timeline in Frame 0 and keyframe it's Delta Rotation by pressing the i key, then move the timeline to the last frame of your animation and do the same, keyframing the last Delta Rotation again.
This will do nothing on its own, you now have to adjust it in the Graph Editor.
Either open a new Graph Editor area, or switch to one of the default screen layouts for Animation which will automatically set up the editors for you.
Now in the graph editor, with the select the shuriken as active object, select the animation curve handle for rotation in the last frame and move it up or down, depending on the direction you want it to rotate, the amount of degrees you want it to spin (amount of turns * 360 degrees), you will probably have to eyeball it to see what looks best, but probably a very high number.
To make the speed constant turn all animation handles into Vector type.