I don’t think there is any way at present to migrate from different cloud services. Unless Flickr has a download tool you would need to add files manually to LRCC.
You can share albums or ad hoc groups of photos or you can present a group of albums as a single link from the LRCC web interface. However the images are only viewed by people you send the link to. They are not generally publicly discoverable like Flickr or SmugMug.
You may miss public groups & comments but you could gain the ability to have everything instantly available on mobile tablet & phone devices.