The latest projections I saw for Henri is that it will be right at hurricane strength when it hits, maybe just above or maybe just below.  That's a serious storm.  They are usually pretty good on their projections but those things can do strange things as they hit land.  Usually they slow down a bit but occasionally one intensifies.  Don't be surprised if the center jumps several miles, probably to the east.  So stay on your toes and pay attention to what is going on.
Have you had thunderstorms or other winds in the range of 75 mile per hour winds?  I'm not trying to downplay them, that is still a dangerous wind, but have you already been through winds like that?  I once lost a shed roof to straight line winds in a thunderstorm when I was in Arkansas, the guy who built it did a bad job.  But you may have already been through winds like that so you have a baseline on how the coop will do. 
I've been through several hurricanes in Louisiana and twice got a new roof because of a storm.  My outbuildings have been OK though.  How well your coop does will depend on how well it is built and how well it is anchored to the ground.  Wind direction will depend on where you are located from the center.  As I said that center can change but if you can put a guy wire to anchor the coop that can help a lot. 
There are three things about a hurricane that cause damage.  Storm surge can be really destructive.  How bad that is depends on your terrain and how close to the sea you are.  You say you aren't worried about that.
If the storm is moving slowly it can dump a tremendous amount of rain.  Hopefully Henri will move fast enough so that isn't a major problem.  You will get heavy rain, some people will be flooded.  That rain will come in bands..  Don't think just because it slacks off that it is over with.  Another band will hit.
Then the wind.  Roofs will be damaged.  A lot of trees will be blown over or limbs will come off.  A lot of people will lose power.  Roads will be blocked.  Anything lose can become a missile.  It sounds like wind is your greatest risk.  Don't be surprised if cell towers go down and you lose communications. 
So what can you do to get ready?  Pick up or secure anything that may become a missile.  That might be hanging baskets of plants, kids' toys, yard decorations, whatever.  I move one car in the garage and park the old one next to the house where it is at least partially protected.  Expect to lose power so get non-perishable food.  Have plenty of drinking water, maybe fill a bathtub so you can flush the toilet.  Ice can be very valuable, start freezing extra.  Down here we'd board up our windows but we have them more often than every 30 years, most of us are prepared.  If you have a generator crank it up to make sure it works and have fuel handy.  Top off your car with gasoline so you can leave if you need to.  There is usually a run on gasoline, lines are long and they may run out. 
Now, finally to your question.  How well do you trust your coop?  It looks pretty strong to me.  Even if a roof blows off that is not likely to harm your chickens, just expose them to rain.  I'd leave them locked in the coop/run mainly to help protect them from flying debris.  I think that will give them an excellent chance to survive.