This movie has a very strange vibe to it, which I think can be attributed to the fact that I've never seen an even reasonably clear copy of it. I own this on DVD and have streamed it from a couple of different sites and the picture quality has made it almost not watchable in every instance.

From what I have been able to see, a group of explorers visit an island of natives in the South Pacific who fear and worship a god called "Gappa". So this is basically stealing from the original "King Kong". Eventually they find an egg that hatches, producing a cute baby Kaiju. Against the natives wishes, the explorers take the baby back to Japan. Then, a Mom and Pop pair of kaiju, that look like a cross between Rodan, Godzilla, and Woodsy the Owl, attack Tokyo or some semblance of a Japanese city. This is more or less a swiping of the plot of the British monster flick, "Gorgo".

The attacking kaiju couple wreak havoc and cause mass destruction until the stubborn cradle robbers give the baby Gappa back to its parents. Once reunited, the baby Gappa is taught how to fly by spreading its wings. This lifts it and the grownup Gappas off the ground, where they glide without ever flapping their wings, into the sunset.