How do I print an individual field in block.html.twig?
If you have a field called field_test you schould be able to do like this

{{ content.field_test }}


and if you want to only print the value you can do like: 

{{ content.field_test[0] }}


If you want to see what is inside the field you can do like this:

{{ kint(content.field_test) }}


But only if you have Devel module installed and have Devel Kint enabled you should be able to do that.

Hope this helps :)