It is not that easy to get a good picture.
I took a picture of my crimson crescents using a digital camera (Canon IXUS), with the camera set to macro (close up), and also holding a small flashlight in the mouth for illumination (my pic is the second one in the post at the start of this thread). It is a bit easier with digital camera, because you can put the camera lens inside your mouth, and the camera's macro setting lets you move in close yet remaining in focus.
You can use a smartphone camera, though, but it takes a little perseverance.
The hardest thing is getting your tongue low enough and out of the way so that you can get a good view of the whole arch of the soft palete. I found if you open your mouth wide as if to start a yawn, that helps to move the tongue downwards so that you get a better view of the arch and the crimson crescents.