I'm going to a concert. Is HD photography allowed?

Every time I go to a concert at my local theater, they threaten to take away my camera so I end up hiding it and sneaking it in. I'm going to another venue in NYC and it says on their page

Q: What is appropriate etiquette for attending?
A: No flash photography or audio/video recording of any kind is allowed.

Does this mean I can simply turn my flash off and it will be OK to take photos with my Canon or do I have to use my iPhone? (I'm bringing both my camera and phone just incase)

HD isn't a photography term - it is about video.

Apart from that, this whole concert photo idea really isn't a good one.
First of all, you may not be allowed to bring a camera into the venue, normally IF they allow in any cameras, then only little P&S ones.
You might get away with smuggling it in, but personally I hate the possibility that I might either have my camera confiscated, or I won't be allowed inside.
Next problem is that concerts are a low light situation, usually also coupled with much movement as well as a fair distance from the subject.

All up, that makes it EXTREMELY challenging. The only hope of half decent concert photos are good DSLR cameras and even for those you need very good and very FAST lenses.

Small P&S cameras have tiny little sensors, so they don't do well with low light situations.
Concert photos are often blurry because there isn't enough light, so the shutter speed is too slow to hand-hold it, even worse when you add the movement of the performers to it.

You could try raising your ISO, but that will add noise to your photos.
You could try using your little flash, but it can't reach very far, and won't do you a whole lot of good other than lighting up the back of the heads directly in front of you.

I'm afraid there are a number of good reasons why the pro's carry around huge, expensive cameras, lenses, and lights.
It would be lovely if a tiny camera could do it all, but the reality is that small P&S's just can't handle concert situations very well. Some places do allow small P&S cameras (but no DSLRs). The reason for that is because they KNOW you will never get any decent shot with a little P&S.

However, I do realize that some of us a lot easier to please than others, so perhaps what is totally unacceptable to me might be fine in YOUR eyes.
If you can't have a good camera with you, at the very least make sure you learn how to you use what you have, so you can make the most out of it. Read your manual several times, attend a class, read some books on photography - it will help a lot.
If you're not interested in learning much, at the very least learn how to turn off the flash. Those tiny on-camera flashes only reach a few feet, so all you do with it is illuminate the bodies in front of you.

As to sound - there's a good reason why the audio pros carry around a lot of very big and very expensive gear. Even a good camcorder can only do so much in that regard - let alone a little P&S still camera! Don't expect miracles - don't even expect anything you'd ever want to listen to again.