You usually can’t fully “fix” direct on-camera flash in post, but you can often improve it.

Useful adjustments mentioned in the answers:

• Levels or curves: Darken washed-out images by moving the black point or shaping contrast with curves. If only part of the image is affected, apply the adjustment with a mask so you darken just the problem areas.
• Burning selectively: Use dodging/burning carefully to reduce bright hotspots and add depth. In Photoshop, a common non-destructive method is a 50% gray overlay layer and painting to darken where needed.
• High-pass filter: Can help restore some perceived detail and reduce the soft, washed-out look when applied subtly.
• RAW processing: If you shot RAW, highlight, tone, and color adjustments are much more flexible, and sometimes that alone is enough.

One answer also suggests a stylistic option: if the flash look is too strong to hide, lean into it and make it look intentional—hard, flat, glam/paparazzi style—by pushing highlights and treating the look as creative rather than corrective.

In short: recover tone first, then use local masks/burning to reduce flash hotspots, add subtle contrast/detail, and accept that some images may work better as a deliberate stylized look.