Using fridge for slow rise dough with eggs

From a food safety perspective, 48h in the fridge will be perfectly safe. (You may want to check out our generic post on storage times.)

Whether it’ll work with regards to intensifying or improving the flavor, I can’t say. Remember that the “more flavor” in regular slow-raise bread is based on enzymatic activity in the flour - which you don’t use. It may or may not be happening in the oat fiber and flax seeds. An experiment should answer that.

Yes, it would be safe, but I'm not sure whether you'd see a difference in flavor.

For the record, I'll list a general "base" recipe that I'll then make recommendations about.

This is based on Diedra's Ultimate Keto Bread v2.0:

finely ground golden flaxseed meal (ƒ)     26.52%     83.0 g 
oat fiber (ƒ)                              26.52%     83.0 g
vital wheat gluten (ƒ)                     46.96%    147.0 g
½ tsp xanthan gum                           0.48%      1.5 g
1 tsp table salt                            1.92%      6.0 g
1 Tbsp instant yeast                        3.31%     10.4 g
1 tsp honey                                 2.24%      7.0 g
1 cup water                                75.72%    237.0 g
2 large eggs                               31.95%    100.0 g
2 Tbsp unsalted butter                      9.06%     28.4 g
                                 Yield    224.66%    703.2 g
                           Total Flour    100.00%    313.0 g

ƒ: this is considered part of the "flour"

In all my testing, the only thing fermentable in this recipe is the honey (meaning none of the flour ingredients are fermentable). The point of the honey in this recipe is to provide the sole source of food for the yeast. In most keto/low-carb baking like this, we usually only get one attempt at a rise, especially since there's a very limited supply of food. So, the question then, is whether a longer-cold ferment in the refrigerator might provide for better taste than the hour room-temperature ferment that the recipe calls for.

With the recipe as-is, I don't think you'll see much of a difference (though I haven't tested this extensively by using long cold fermentation times). The rather limited supply of food will likely be used up within the first couple hours of the cold ferment, and not much would happen after that.

It could theoretically be possible to sub in a small amount (10 - 20 g or less) of whole wheat flour or other fermentable flour in place of the honey to serve as a long-term source of food for the yeast during a cold ferment. It would be tricky though to determine how that might affect the overall net carb count (determine what percentage of the carbs were "consumed" by the yeast).

In lieu of that, there are a couple things you can do to improve the flavor and texture. First, leave out the xanthan gum, especially if you have a stand mixer or can successfully knead this by hand (it takes a dough scraper to start and a bit of practice, but it can be done). The xanthan gum overly-inhibits the gluten development and results in a tighter more dense crumb. The mucilage from the flaxseed, the butter, and the eggs are all you need to successfully weaken the gluten without over-doing it. Second, to offset the taste of the oat fiber (basically like cardboard with a slight hint of Cheerios), add 2 Tbsp or so of sweetener. I prefer Splenda or 1 tsp or so of liquid sucralose. Third, use ½ cup of water, and ½ a cup of buttermilk (a low-carb form of regular milk). The buttermilk* adds a depth of flavor that leaves water-only variations seem bland in comparison. Despite its acidity, it does seem to help a bit in browning of the bread as well. Fourth, up the salt to around 2.35% (1 tsp + scant ¼ tsp, or 7.3 g). I also upped the yeast slightly.

So, the revised recipe:

finely ground golden flaxseed meal (ƒ)     26.52%     83.0 g 
oat fiber (ƒ)                              26.52%     83.0 g
vital wheat gluten (ƒ)                     46.96%    147.0 g
1 tsp + scant  ¼ tsp table salt             2.35%      7.3 g
3 ½ tsp instant yeast                       3.31%     12.1 g
1 tsp honey                                 2.24%      7.0 g
½ cup water                                37.70%    118.0 g
½ cup buttermilk                           39.14%    122.5 g
2 large eggs                               31.95%    100.0 g
2 Tbsp unsalted butter                      9.06%     28.4 g
                                 Yield    227.37%    711.7 g
                           Total Flour    100.00%    313.0 g

* Regarding the carbs in buttermilk (and yogurt): While the nutrition info for 1 cup (245 g) of buttermilk and 1 cup (245 g) of whole plain (unsweetened) yogurt will say around 12 g of carbs from sugars, in reality, that number is actually much lower. The reason for this is that most of the milk sugar (lactose) in buttermilk and yogurt has been converted by the bacteria culture to lactic acid. As doctors Jack Goldberg and Karen O'Mara explain in their book "The GO-Diet", you can count a cup of either of these as 4 g of net carbs rather than 12 g. (See this website for more info: http://www.lowcarbluxury.com/yogurt.html). So, the ½ cup of buttermilk would only add around 2 g of net carbs.