The pilot of the amphibious float-equipped airplane reported that during the initial climb from an airport runway, he was distracted by other airport traffic and forgot to retract the landing gear. As he approached his destination, which was a lake, he stated he did not perform the before landing checklist as he usually does, and failed to notice that the landing gear was still down. The pilot reported that his touchdown was smooth, but the airplane immediately nosed over and he felt "a fire hose of water" come through the windscreen. After the airplane came to rest, the pilot reported that he was submerged underwater, but was able to remain calm and slip out the pilot side window. The fuselage sustained substantial damage. The pilot stated there were no mechanical malfunctions or failures with the airplane that would have precluded normal operation.