This integration is in the beta version.
To use Dynamic Shortcodes on Gutenberg, first ensure the plugin is enabled inside Gutenberg Blocks Content (in the plugin dashboard Settings). In most cases, you should also disable it in the Post Content and Text Widgets, as they are superfluous with Gutenberg.
You can insert Dynamic Shortcodes (DS) on most blocks usually, but there are some exceptions, including:
Button Block URLs
If you insert a DS in the Button Block URL, WordPress thinks the https:// part (the protocol) is missing and will add it automatically. This will likely cause problems as your DS will already have the protocol. To solve the problem you have to switch to the Gutenberg Code Editor and remove the https:// just before the DS from the code.
Images
You can use a DS with the image URL, but the image will currently not be visible in the editor. In its place, you'll see the default alt attribute. The image will be visible in the front, though.
Embedded Blocks (YouTube, etc.)
It's currently not possible to use DS with these blocks.