What is the importance of the following quotation from "A Worn Path"? "Without warning, she had seen with her own eyes a flashing nickel fall out...

I do not think that the quotation itself has that much importance, but the nickel does.

Phoenix will, in a little while, pick up the nickel.  In a sense, her taking the nickel gives her a small amount of revenge on the white man.  He treats her very badly.  He makes fun of black people, saying they can't resist Santa Claus.  He threatens to kill her.  She gets some small revenge by taking the nickel.

Seeing the nickel also shows how venal and dishonest he is when he tells her he has no money to give her.

I'd give you a dime if I had any money with me.

Finally, it allows us to see Phoenix being somewhat honest -- admitting she has just done the man some unspecified wrong:

"No, sir, I seen plenty go off closer by, in my day, and for less than what I done," she said, holding utterly still.

Thus, the nickel allows Welty to comment on the way that whites treat blacks and, in this case, the relative morality of the white man and the black woman.