Here are the only two pictures of him that I have:
I never met my grandfather, so I'll just tell you what I know. He was born in N.C. in 1915 and was a paratrooper in WWII. Going by the photos, it seems he was a staff sergeant, and I think the patch with the "5" indicates the US Army North. However, his obituary states that he served with the 509th Parachute and Infantry Battalion. I have seen a couple of letters that he sent to my grandma from Italy recounting the Anzio landing, but my knowledge pretty much stops there. From what I've read, it's possible that he was also in North Africa prior to the Allied invasion of Europe. I have attempted to obtain his military records, but apparently a fire destroyed whatever I was looking for. If you guys need any more info, I'll try my best to provide, and thank you!
Wikipedia- https://en.wikipedia.org/wiki/509th_Infantry_Regiment_(United_States) - can at least corroborate what you already know.
Depending on when he enlisted he would have participated in Operation Torch in North Africa, and the 509th did indeed participate in Italy. From there he may have participated in Operation Dragoon in Southern France, and then finally the Battle of the Bulge. Which in itself may explain why you don't know much about it- I don't think too many Americans were terribly eager to talk about their experiences from the Bulge.
There's also a website dedicated to the 509th. Although it's maintained by a living history group so it's hard to say if they're super serious about their craft or just LARPing dorks. You do honestly see the full range in these things from people who will perform historical reenactments with incredible attention to authenticity and sometimes it's just people who can't accept the South lost the War.
Finally- and perhaps what is of most interest to you- is the website that the 509 appear to maintain themselves. This website does confirm that a Henry K. Kirkpatrick served with them. I don't know how much you want to stare at grainy old photos and WW2 era video reels but they have a fair amount of media you can pour over as well as highly detailed accounts of their action in WW2 that would outdo anything I can do here, so I'll just direct you to them.
Was there anything specific you were looking for?
Hello there! As your question is related to looking for identification/information regarding military personnel, our Guide on Military Identification may be of use to you. It provides a number of different resources, including how to request service records from a number of national agencies around the world, as well as graphical aids to assist in deciphering rank, unit, and other forms of badges or insignia. While the users here may still be able to lend you more assistance, hopefully this will provide a good place to start!