Use an Easy Out, also known as a Counter Sink. It is a cone shaped hardened bolt with sharp threads that go in a reverse. You insert the counter sink into the hole and then hit it a couple of times with a hammer to cut the threads into the bolt head, then put a socket on the hex head, or a wrench on the square head, and turn the bolt out. A set can be purchased at any tool store, and should be part of every shops tool inventory.

Sometimes you may need to drill the center hole a little deeper to give the easy out enough depth for the threads to get a really good bite on the stuck bolt.

Google "Easy Out" to get a picture of the tool you need.

Heat it with a torch a couple of times to allow the heat to migrate to the threads. Hammer the fluted socket onto the bolt. Don't use an impact wrench...remove it by hand.

if the easy out doesn't work and you haven't messed up the head any more - Use a dremel tool and cut-off wheel to slot the head and use a screwdriver (Impact driver would be best to break it loose).

Get an "Easy Out" (screw extractor) set, or single (but sometimes you have to go to the next bigger one on tough removals, and individual prices are higher per piece than a set anyway) - if you don't have a set laying around, you should have one if doing much of any mechanical repairs. The use of one usually justifies the cost of the set (trust me), by saving time/hassle. Should work particularly well with this piece - you might need to drill a hole in it to get it deep enough to grab.

I would try "whacking" the head with a small hammer first - hard enough to give it a good jolt (loosen up any corrosion/build up residue that might be holding the threads tightly), but not hard enough to do serious damage - mainly to other stuff than the screw. Might want to use a punch that fits inside the hole - or covers the whole outside, to prevent an off-target hit - and/or to enable an easy strike (can't see how much room you have around it to swing).

Try penetrating oil and leave it on for about 15 mins or heating it up with a torch. Use the vicegrips.

Shops out of ideas and we need this flex hose off 1200 any ideas are appreciated. The picture is what we are working with.