Thanks for an interesting question. There are two ways to accomplish your goal.
The WP_Query Class Reference lists several Tag Parameters. If you know the term ID values for the tags you want you can use them as follows:
[mla_gallery tag__in=333 tag__not_in=380]
There is also mention of a tag_slug__in
parameter, so you might try:
[mla_gallery tag_slug__in=birds-of-india tag_slug__not_in=kadi]
Sadly, there is no tag_slug__not_in
parameter, so this fails. You can use the more powerful Taxonomy Query to build a query with slug values:
[mla_gallery tax_query="array(array('taxonomy'=>'post_tag','field'=>'slug','terms'=>'birds-of-india'),array('taxonomy'=>'post_tag','field'=>'slug','terms'=>'kadi','operator'=>'NOT IN'),'relation'=>'AND')"]
The above examples use tags from my test system, but they should work fine with the proper term substitutions for your site.
I am marking this topic resolved, but please update it if you have any problems with the above suggestions or further questions about queries on taxonomy terms. Thanks for your continued participation in the Support Forum.