Little to nothing. You have to understand the WHO is a voluntary organization to follow any of its recommendations or guidelines. It can be useful in some situations and it can be not useful in other situations. At the end of the day it is simply a way for many countries to collect information together and to provide health advice and resources mainly to those countries who lack sufficient ability to do it on their own.

So for the United States directly there would be little to no effect. Depending on how this impacts the United States interaction with other countries and the dissemination of support and health information and health research there could be impacts for other countries.

One thing to keep in mind with the last major pandemic, several years ago, much of the WHO advice on how to deal with it was largely ignored.

More discussion: https://news.ycombinator.com/item?id=42775602

Most immediately, America will look like a chicken with it's head cut off for the next four bird flu seasons.