Phoenix is a colorful character, both literally and figuratively. As well as having a red rag tied around her hair and strange golden inflections in her skin, she's so old she's almost ageless. Just like the phoenix of ancient mythology, the old lady seems to have been around since the dawn of time, which makes the bright colors of her skin and clothing all the more remarkable. There's life in the old girl yet.
If Phoenix were just a regular little old lady, then Welty would not have described her in the way that she did. By emphasizing the colors associated with the mythological phoenix, Welty is highlighting the personal qualities of this remarkable woman, whose unprepossessing demeanor belies her great wisdom.
The mythical phoenix had red and gold feathers. It lived a long time and, in its old age, built a next that it then started on fire. The old bird was burned up and a new bird reborn in its place.
In "A Worn Path," Phoenix is quite old. She wears a dark dress, but a golden color shines through from her skin, and the second paragraph tells us "and the two knobs of her cheeks were illumined by a yellow burning under the dark" (she burns like a phoenix).
She also is reborn in some ways, or is working to help others be reborn. She was a slave, but is free. Her memory dies, but comes back. She is old, but is buying toys for the young.