The VA has said that veterans affected by Hurricane Harvey don't need to worry about their GI Bill benefits.
In a statement on the GI Bill website, the VA says that "If your school is, or was, temporarily closed due to Hurricane Harvey, VA will consider your attendance as continuous and your payment will not be affected." This means that you will continue to receive your housing allowance even if you cannot attend classes. Veterans using the Montgomery GI Bill must verify their attendance online like normal to receive payment.
Of course, this comes with some fine print. If you are enrolled, and the school hasn't sent your enrollment to the VA yet, you are out of luck. You won't get any money until classes resume. Also, if the school remains open, or opens later but you cannot attend due to hurricane related issues, you won't get any GI Bill payments.
For more information you should contact the VA at 888-442-4551.