Wrap with foil after you let it rest a few minutes to avoid too much carryover heat. Then, overwrap with a few towels and pop it in a cooler and leave it alone, you will be fine.
Some folks heat a firebrick and put that in the cooler too, not a bad idea but, I’ve never done that.
If your worried leave a probe in it. If it's above 140 it's safe. Another method is to preheat your cooler by putting hot water in it to warm it up, and then dumping that out to put in your brisket. It's not an option right now, but leaving the cooler out in the sun can help. 6 hours is a long hold but not unheard of. I've gotten 5 pretty easily but I don't remember if I was venting my briskets back then.
It'll stay above 140 degrees F, outside of the bacterial risk zone. Not only will this carry your brisket to dinner, I'd suspect it'll be one of the best ones you've made due to the very long rest. Don't open the cooler until you're ready to serve, though, you'll lose a LOT of heat every time it's cracked.
Personally, I plan for a minimum of 2 hours in a cooler, and don't even blink twice at 4 hours. 6 hours is not a problem.
Like the others said, I also think you should be fine. I once put a probe in the brisket before closing it in the cooler and never got lower than 160 in four hours. I typically fold a couple of towels in the bottom and then add a couple slightly snugged around the top. With it foil wrapped, it would be hard-pressed to dry out -- more likely to stay moist.