This plugin currently adds Reactions Buttons using “the_content” hook, so if you are using a gallery plugin that respect standard hook usage it should work. (i.e. if you enable Reactions for Media content and visit any Attachment page the buttons are there).
You don’t even need to buy the plugin to test your galleries, you may use the free version: https://wordpress.org/plugins/da-reactions/
Reactions in free version are available for Posts, Pages and Media files, since Galleries are made of Media files it may be enough.
Remember that you have to enable buttons on General Settings Page if you don’t see them.
Unfortunately a quick test on NextGen was unlucky, but since it is a very common plugin I will attempt to make it work in next release.
Please send me feedback and bug report on free version, because I’d like to improve this product.