I'm surprised that someone finds flaxseed meal objectionable. I mean, I toss some into bread, and other than being visually noticeable, the flavor isn't incredibly different.

I hope your challah comes out well, whenever it does (I make myself start the dough before work, so it can go into the oven soon after I get home, then move on to the milichig/fleishig things after that).

Shabbat Shalom!