Monjon,
Your very welcome!
I take 2 pkg of either the Tortillas/Whole Wheat Pita/Whole Wheat Wrap Bread ( very thin like tortilla) for 2 week trip, 1 piece per day.
They usually come about 8 per pkg. In Mid-May when I normally go, they stay good for 4-5 days once open and if kept as cool as possible.
After that they get a few green spots, which I tell myself is penicillin, and I eat them anyway ;D
 So, I would take Drewfus's idea about the expiration date, PLUS I would repackage the bread in a vacuum seal bag, say 4-5 days worth for the two of you. I use plastic Sterilite boxes in my food pack, and so I made a protective cover for the round flat breads. I took 2 pieces of flat cardboard and duct tape 3 sides and put the bread in. I then stand the cardboard on end and on the outside of box. This keeps them from getting mashed.

Drefus:  Knowing the government, and the shelf life of Hardtack, I would be surprised if the stuff you had in your MRE's WAS from the 60's :'(  In the 60's with the Vietnam war raging, they tried to keep cost's down.  2x a week we had WW2 era K rations made into cafeteria lunch!  They took the condiment packages and put them out on a table for anyone too take.  Everybody smoked in the WW2 era, so they had a 4 pack of cigarettes in the K rations.  I smoked for a couple of years while in the service, as most of the guys did. These 4 packs of cigarettes were Lucky Strike GREEN and were non -filtered ! Not only were they 20+ years old, they were so STRONG, we smoked them to get a nicotine BUZZ ;D  If you were man enough to smoke them, you were man enough for just about anything!