The Beta of ACF 5.8 lets you create Gutenberg blocks with custom fields.
You can preview these block in the editor. Sadly, you have to be an ACF-Pro customer to use the beta.
Otherwise you could try to fetch the custom fields via the REST-API utilizing this plugin: https://github.com/airesvsg/acf-to-rest-api/
Refer to this answer on how get the current Post ID in Gutenberg.