The flashed picture looks fine. Instead of directional flash, try bouncing the flash behind you or even bouncing it from your right or left side or even into a corner across from the subject. You'll see how diffused it will be.
The high iso helps to get a shot u would normally get that looks like flash is the main source but with high iso, you can blend what ambient light you have with the flash making it look more natural.
The pic u posted with no flash shows how low the ambient light really is if u bumped it to 6400 and still looked horribly dark but at least the blend with flash will look more natural. If in that situation the ambient was another two stops brighter, u could have lowered your flash exposure at least a stop to make it look even more natural, providing you also diffused the more than your directional light which is very specular in outcome.
This is why i prefer to bump iso and blend it with ambient. It looks a world better. Always expose a third extra when using ISO that high and you can lower the exposure a touch back in pp and it will hide the grain even better. And using high iso also will allow u to step down the aperture for better sharpness as well. If you have a 2.8 lens, shooting it at 4-5 would make things sharper and usually u will see the grain in the out of focus areas but not so much in the areas in focus.
Break free of the fear of grain. Its a different world altogether with blended ambient/flash picture vs only flash because ur afraid of grain. I don't even use any nr in pp ever. Just expose properly. Well lit makes all the difference to convey "feel"