Timelines should do the trick. I think this may be what you’re looking for (though the example is very different, the concept should be the same): UE4 flickering lights
I don’t think there’s any way to directly export all those light animations, unless you want to write up a Blender add-on yourself (in which case please share with the rest of us!).
Cool Blender animation by the way, that’ll look awesome in UE4!