wp_link_pages appearing after post content and not at bottom of page

Your call of wp_link_pages displays navigation immediately because echo argument is set to 1 by default, and it means to echo result. So try to add &echo=0 at the ennd of wp_link_pages call:

add_filter ('the_content', 'pagination_after_post',1);
function pagination_after_post($content) {
   if(is_single()) {
      $content.= '<div class="pagination">' . wp_link_pages('before=&after=&next_or_number=next&nextpagelink=Next&previouspagelink=Previous&echo=0') . '</div>';
   }
   return $content;
}

Read more about wp_link_pages parameters in codex.

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