How to add more Display Suite template suggestions
The problem actually wasn't in ds-1col--search-result.tpl.php. It was when I suggested a custom template for a node when I was doing quick tests, with print $ds_content; in them, the nodes which didn't have the search_result view mode configured, weren't being preprocessed by display suite hence didn't have the $ds_content variable set which was being printed on the custom template. Hence it gave me the impression that it wasn't working. 

But to answer the question, there's no special stuff you need to do to suggest a template for display suite. First copy the template from display suite folder to your themes folder. And then all you have to do is use the normal hook_process_node and suggest that template for a certain view mode.