set a user-meta key as avatar

<?php
$id = get_current_user_id(); // this is for the current user, for other user just change this variable to the user id intended
$link = get_user_meta( $id, 'avatar', true ); ?>
<img src="<?php echo $link ?>" alt="">

That is your answer, but if you want to understand it just continue reading!..
(only after writing everything below I saw that your meta_key had the name “avatar”, anyhow..)

This are 10 lines of my wp_usermeta table;

mysql> select * from wp_usermeta limit 5, 10;
+----------+---------+-----------------------+---------------------------------+
| umeta_id | user_id | meta_key              | meta_value                      |
+----------+---------+-----------------------+---------------------------------+
|        6 |       1 | syntax_highlighting   | true                            |
|        7 |       1 | comment_shortcuts     | false                           |
|        8 |       1 | admin_color           | light                           |
|        9 |       1 | use_ssl               | 0                               |
|       10 |       1 | show_admin_bar_front  | false                           |
|       11 |       1 | locale                |                                 |
|       12 |       1 | wp_capabilities       | a:1:{s:13:"administrator";b:1;} |
|       13 |       1 | wp_user_level         | 10                              |
|       14 |       1 | dismissed_wp_pointers | theme_editor_notice             |
|       15 |       1 | show_welcome_panel    | 0                               |
+----------+---------+-----------------------+---------------------------------+
10 rows in set (0.00 sec)

If I want my admin_color (3rd line) I can run this code:

$link = get_user_meta( 1, 'admin_color', true );
echo '<p>'. $link . '</p>';

and this prints me “light”, the meta_value, where your link path will be.
The first argument is the user_id, the second the meta_key and the third is to say if you only want a single result or more, default is false, this means only one result, in this case true means as much as they are in the table.

This to say that you can use this function, but you need to know the meta_key value to get the meta_value, because the user id has a lot of meta_keys, and the meta_key is unique. to know the meta_key you can use this code, analize it and then change the user_id to your user_id and the meta_key to your meta key, and you will get your link path.

$id = get_current_user_id();
echo 'My id is '.$id;
$link = get_user_meta( $id, '', true );
echo '<pre>';
print_r($link);

now if it is there just use the first code with the proper arguments

<?php
$id = get_current_user_id();
$link = get_user_meta( $id, 'your_meta_key_target', true ); ?>
<img src="<?php echo $link ?>" alt="">