How to store chicken breasts for cooking

Ok, so I'm not really sure what you're saying here... are you looking for a cool chicken breast or a hot one? I'll try to cover both.

First things first, completely twice-cooking chicken breast, (unless the second cooking method is braising or stewing) is a road which only leads to dryness. You can try to mitigate this dryness by just barely heating the chicken through on the second cook, but the best you're probably going to do is get 'less dry' rather than 'juicy.'

If you're looking for a cool poached chicken breast but just want that nice grilled flavor, you should give it a hard sear on the grill without cooking it through immediately before you poach it, and then use the smallest amount of liquid that you can to avoid diluting the grilled flavor too much. This method ensures that you only completely cook it through once.

If you're looking for a hot chicken breast, the approach is different. Burger places that make grilled chicken sandwiches either a) grill them to order, b) grill them and then hold them at about 140 degrees until they're ordered, or c) par cook them and finish them to order. Some lower quality places might grab the cooked chicken they have as a salad condiment to put on a pizza or into a saute or on the griddle for a hot chicken sandwich— those are the kind of places that don't care if they serve you dry chicken.

Larger pieces— like spatchcocked grilled smaller chickens or half-roasted chickens— are often par cooked, which means they're partially cooked and finished to order. Any place I've seen that par cooks chicken well does so within an hour or two of when they expect to sell them and doesn't refrigerate them before cooking. The birds that are par cooked and not ordered generally get finished before they're supposed to be thrown away (2hrs according to the FDA food code) and repurposed (perhaps as chicken salad for the next day's lunch, chicken soup, or chicken pot pies.) Par cooking, cooling, and finishing is probably only marginally better than twice-cooking for the meat towards the outside.

Edit: Saw your comment above. I really do think your best bet for cooking chicken sandwiches on the grill is just doing it to order. If you need to do it fast, pound them out or butterfly them first, then grill them. If that's just not doable for you, I recommend trying sous-vide cooking the chicken, which can be MUCH gentler than poaching. You can pasteurize the breasts at a low enough temperature that you don't tighten up the muscle fiber much, cool them extremely rapidly for safety, and then keep them refrigerated for a few days until you're ready to use them.