It may sound too simple, but best result I get is when I desaturate the red part, leave the selection there, and push (as in darken) the selection.
Better still: don’t flash direct, but put some "silk" foil over the flash. I mean the brushed type of silk. Put it over the flash with the brush strokes horizontal, so that a significant portion of the light goes toward the ceiling.
Give your photos a professional finish with sharpening in Photoshop. Learn to enhance details, create contrast, and prepare your images for print, web, and social media.
Related Discussion Topics
Nice and short text about related topics in discussion sections