The clone tool is used to replicate selected parts of the image, which can effectively help you cover up undesirable spots, marks or abrupt shade variations. The same can be used to remove camera shine by covering it up with another part of the same image. Select the clone tool from the toolbar on the left and press the ALT key on your keyboard before clicking anywhere on the photo to select a region you want to clone. Now you can paint over the camera shine normally and the region you selected earlier will be copied there.
You can also play with image variations to reduce the strength of the camera shine. Open up the variations box from the Image>Adjustments menu and play with the sliders to modify lighting, color and hue etc. You can reduce the brightness as well, or increase the contrast to make the camera shine less visible.
Photoshop also supports third party plug-ins which can be used for various effects. Professional photography plug-in packages often have the remove lens flare option. If you can download and install one of these, you can easily access it to modify the image with one click using the filters menu.
If the camera shine is not affecting an object in the image, you can always use the crop function to remove the undesirable effect from the image.
Finally, if the camera shine, or lens flare is too strong and hard to remove, you can remove all color from the photo using the ‘de-saturate’ or turn to grayscale option. This will effectively render the image black and white, weakening the shine or flare’s strength.