How to allow .xls file uploads?

Try the same function but different $mime_types key ('xla|xls|xlt|xlw'):

<?php
function my_myme_types( $mime_types ){
    // New allowed mime types.
    $mime_types['xla|xls|xlt|xlw'] = 'application/vnd.ms-excel';

    return $mime_types;
}
add_filter( 'upload_mimes', 'my_myme_types', 1, 1 );

To get MIME type array keys and values used by WordPress:

<?php
$mimes = wp_get_mime_types();

echo '<pre>';
print_r( $data );
echo '</pre>';