Bringing food into the US

Might be easier to just order either the flour or the brown bread mix online. I see several sellers on Amazon who appear to offer what you're looking for.

Been there, done that and it isn’t the same quality. The best flour I have tried so far is from the north, Neil’s Wholemeal Course Flour.

You have to Declare it as with all other food at the US CBP checkpoint, and they will let you know if it is OK. I don't see it on the USDA prohibited list, but there's always the possibility that at the time, there may be some current disease or insect threat they are guarding against.

King Arthur sells an Irish-style wholemeal flour. Of course, the recipe could make all the difference, too.

I bought four bags of the King Arthur flour that you describe. While better than other US processed flour, it does not come close to the real deal.

In pouring over the USDA regs, it appears that I can bring a reasonable amount for personal use. I will declare it.

Thanks to all.

“Travelers entering the United States must declare all agricultural and wildlife products to U.S. Customs and Border Protection officials. They will determine whether your products can enter the country after checking to make sure they meet entry requirements and do not harbor harmful foreign pests or diseases. We recommend that you keep receipts and original packaging for agricultural products as proof of their country of origin.” USDA

I think the problem would be if you were trying to bring bulk product in like from a mill that wasn’t commercially processed. Good luck, I love the brown bread and it doesn’t quite taste the same here but I keep trying.
And please make sure you declare it!

No problem. On our Ireland trip last spring, I brought home a two kilo package of Macroom stone-ground whole wheat flour, 2 kilos of another whole meal flour, plus 2 kilos of oatmeal. I actually carried it in my carry-on suitcase (I packed light, so that I could fit those in my bag), but if you’re checking your bag, that will work, too. Declare it and get ready to bake with it.

What they care about is animal products such as meat, raw (unpasteurized) dairy products, etc.,; live plant material such as seeds, raw fruits and vegetables; and anything with soil clinging to it. Commercially processed and packaged foods such as biscuits and whole meal flour are fine.

But you still need to declare them.

I'd opt for buying the flour in sealed, supermarket-style bags or other containers rather than buying bulk flour and dumping it into a plastic bag myself. The inspectors seem to prefer commercial packaging.

You can bring wheat flour with you

https://www.aphis.usda.gov/ace/generally-authorized-non-propagative-plant-products
Look under "Other Miscellaneous and Processed Products"

Products not listed in the Miscellaneous Processed Products Manual or the Seeds Not for Planting Manual are unrestricted unless covered under the Convention on International Trade in Endangered Species1, a Federal Noxious Weed, or part of the Federal Seed Act. Below is a list of commonly imported goods that are generally admissible without a permit or phytosanitary certificate... Wheat milled products and by-products: bulgur, couscous, flour, freek. Germ, kibbled wheat, pearled or semi-pearled spelt or wheat, pelted wheat, pollards, puffed wheat, semolina, roasted grain, wheat bran

Travelers may find these two links useful for knowing what may be brought back --
https://www.aphis.usda.gov/
https://www.dontpackapest.com/
Don't pack a pest is a joint effort of USDA, CBP, and FDACS.

No matter what make sure you declare all food and agricultural products you bring back.

I carried 6 one pound packages of coffee home from Mexico, was very anxious on way home, nice man checking my passport at the texas airport laughed and said "coffee is not a concern: