Storing Array from returned database query and using the array in a new query

You need to pass author__in as an array but that isn’t what you doing with this: ( array( 'author__in' => array( $followed ) ) ). You are creating an odd set of nested arrays. WP_Query isn’t going to know what to do with it. A much simplified version should work:

$followed = $wpdb->get_col("
  SELECT user_id1 
  FROM wp_um_followers 
  WHERE user_id2 = 1"
);

$get_these_posts = array( 
  'post_type' => 'stream', 
  'post_status' => 'publish', 
  'posts_per_page' => '10', 
  'paged' => $paged, 
  'author__in' => $followed
);

Notice I used get_col(). That will return a simple array of IDs.