WP-Members 3.1 will include an image upload field that will be able to be used for many things, including user avatars. Since this is a new feature, I expect that it will take a little bit of time before the process is fully mature.
With that in mind as well as considering that not everyone updates to the latest version and that some people just like the WP User Avatar plugin, this post describes a nicely integrated process for a user to update their avatar on the WP-Members user profile screen.
This code snippet will add a link to the WP-Members user profile update screen to update the user’s avatar, and will set up a custom screen for avatar update screen.
The snippet can be used “cut-and-paste” but also has some elements that could be customized. Additionally, the features of the WP User Avatar front end process could have some CSS applied for theme integration. The screenshot here is a demo site using Twenty Fourteen, so colors and buttons will look different for you.
Note: you must also have WP User Avatar installed for this to work.