If you use custom taxonomies in WordPress, they don’t automatically get added to the new Gutenberg block interface.

Fortunately this is an easy fix: you need to add this extra parameter to the arguments you set when you first define your taxonomy:

'show_in_rest' => true

so your taxonomy arguments might look like this:

$args = array(
    'hierarchical' => false,
    'public' => true,
    'show_ui' => true,
    'show_admin_column' => true,
    'show_in_nav_menus' => true,
    'show_in_rest' => true,
    'show_tagcloud' => true,
    'show_admin_column' => true,
);

And your post edit screen should now show your taxonomy: