Hi there! Currently there is no way to embed a Kibana Dashboard in an external web application without using iframes via the embed code feature.
Because Kibana is running over 100 plugins, may of which contribute to dashboard features, it isn't currently feasible to have all of those resources available in a standalone runtime without bringing along the rest of Kibana, hence the need for iframes.
One exception here are Canvas shareables, which are currently in beta. These will allow you to capture a snapshot of a Canvas workpad at a specific point in time, and embed the whole thing in another web app using a code snippet instead of an iframe.