Creating a button from data from Author meta

You just created an empty link, it has correct link but no inner text:

echo '<a href="' . esc_url(     the_author_meta('snapchat_profile')) . '">Follow on Snapchat</a>';

And since you already stored the link in $snapchat_profile variable, no need to call the the_author_meta('snapchat_profile') function once again (it will only reduce in a few bits of extra memory usage and ..) so you should end up with this:

$snapchat_profile = get_the_author_meta( 'snapchat_profile' );
if ( $snapchat_profile ) {
    echo '<a href="' . esc_url( $snapchat_profile ) . '">Follow on Snapchat</a>';
}