To use Dynamic Shortcodes on Gutenberg first ensure that 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.
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You can insert Dynamic Shortcodes (DS) on most blocks normally, but there are some exceptions, including:
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​Button Block URLs

If you insert a DS in 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.
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​Images
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You can use a DS with the image URL but the image will currently not be visible in the editor, in it's place you'll see the default alt attribute. The image will be visibile in the frontend though.
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​Embedded Blocks (youtube etc.)
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It's currently not possible to use DS with these blocks.