X-rays in flexion and extension can show angular instability of the cervical spine as well as hypermobility or spondylolisthesis.
Additional Dens imagining through the open mouth can be useful (Sandberg x-rays).
Moreover imaging in lateral bending through the open mouth can be taken.
A very helpful method is the passiv flexion and extension with the help of the doctor. The doctors expose themselves to the radiation and push the patients head in maximum flexion and extension. This technique has the advantage that the patient goes far beyond the pain and moves further then without the help. Disadvantage of course is, that the symptoms can get a lot worse after.
X-rays do always carry the risk of radiation exposure which is why it is very important that the radiologist knows exactly how to take the images.
X-ray in extension with help of the doctor
X-ray in flexion with help of the doctor