Knowledge on Communities is great, but is a complete PITA to set up. There are so many reasons why your articles may not be displaying.
First, is the community set up right - go through Setting up Knowledge on Communities to make sure you have not missed one of the vital steps.
- Is the Article Detail page visible to the Guest User
- See Audience, Page Variations settings
- Does the Guest User Profile have Read access on the Object for the Article Type
- And the Custom Fields on the Article Type that displays the data that the Guest User needs to see.
- Are the Data Categories visible to the Guest User Profile
- Does the Guest User Profile have access to ALL the Data Categories that have been set on the Article.
- See Salesforce Help https://help.salesforce.com/articleView?id=category_visibility_whatis.htm&type=0for a full explanation of who can see what.
- Has the Article been assigned to a Topic
- Can you navigate to the Article via the URL directly
- Can you search on the Article
- Does it appear in the Article Topic list.