BasePress works with both standard and pretty permalinks according to WordPress settings.
All permalinks slugs are customisable as they use the knowledge base, section and article slugs. The knowledge base portion of the permalink comes from the entry page slug so changing that page slug will reflect on all permalinks.
Below are some permalinks example:
Knowledge Base entry page http://www.yourdomain.com/knowledge-base/
Product Page with sections listing http://www.yourdomain.com/knowledge-base/knowledge-base-slug/
Section Page with articles listing http://www.yourdomain.com/knowledge-base/knowledge-base-slug/section-slug/
Article Permalink http://www.yourdomain.com/knowledge-base/knowledge-base-slug/section-slug/article-slug/
Article Anchor http://www.yourdomain.com/knowledge-base/knowledge-base-slug/section-slug/article-slug/#anchor-slug
Article Pagination http://www.yourdomain.com/knowledge-base/knowledge-base-slug/section-slug/article-slug/2/
Search Permalink http://www.yourdomain.com/knowledge-base/knowledge-base-slug/search/search+terms
If you change the entry page slug you would need to visit the plugin’s Settings page and just click on “Save Settings”. This will trigger WordPress to refresh the permalinks structure and avoid the 404 pages. All other slugs can be changed at any time without breaking the site links and you can switch from standard permalinks to pretty ones whenever you need.