Can slugs from posts and custom post types conflict?

Once you are using POST method, so url is not visible (and search engines don’t take is into account), send the request using query string:

add_query_var( array('post_type' = 'flyers', 'post_name' = 'flyer-01'), home_url() );

In this way the url generated is something like http://example.com?post_type=flyers&post_name=flyer-01 is ugly to see, but no one have to see it… and it works (it should).