I am a natural blonde who dyed her hair red. It's fading pretty well, but parts of it are still a bit darker than the others. I was planning on letting it fade as much as possible before going to a stylist and asking them to try to match my natural color. But... I was wondering if I add a bit of 20 volume peroxide to my shampoo if that would help. I do not want to damage my hair, and if the results will just be streaky, I don't want to do that either. I just want to fade the left over color a bit faster.

I wouldn't recommend putting bleach in your shampoo.  I don't have much experience with this but something I know people recommend is doing a hot oil treatment on your hair.  That might help lift some of the remaining color.

Peroxide is very damaging to your hair, I'd leave that to the professionals if you feel the need.  But before going that route, I'd try oiling your hair to try to lift the color.

From my own experience, I've been told by hairdressers to remember that red hair dye darkens over time. Also, there are some dyes with natural brighteners to maintain a shade for a longer period of time.
I've never heard of anyone using peroxide in their shampoo, that sounds a bit extreme.  :o
But if your hair naturally lightens... maybe you could just use sun-in?