You'll need to publish your family tree on some other service; Family Echo trees are not included in search engines (e.g. Google, Bing,...). Even within Family Echo you can't search for someone's family tree.
You can create a link to your Family Echo family tree. In order to view a family tree in Family Echo, select someone (marked as not died) in the tree, then you click on that person (in your tree), then click the Share link at the bottom-center of the window, and set Permissions to View. At the bottom of the left pane, click the "Create link" button and copy that link. You can then share that link with whomever you wish, but this will NOT make it PUBLIC.