Is there any way to make an egg pancake without sugar or white flour?
You likely need to define 'egg pancake', because to me, it would seem that the ideal solution would be something without flour or sugar at all -- an omelette.

And there are many other similar items that could also qualify, if you want more than just eggs in there -- if you add potato, you can make the Jewish latkes (aka, 'potato pancakes') or Spanish tortilla de patatas.  If you used mashed potatoes and a little bit of a flour (not necessarily wheat), you could make French matafan (which looks more like an American pancake).

If you add shreaded vegetables, and mayme some sort of flour (again, not necessarily wheat), you can make the Japanese okonomiyaki or the Korean jeon.

If you use cornmeal instead of wheat flour, you can make the New England (likely Native American in origin) jonnycakes -- some recipes call for sugar and/or some wheat flour, but there are plenty that don't.

If you're really set on using oats, then look for recipes for Scottish oatcakes (again, some recipes call for sugar and flour, but not all).  Although they're cooked like a pancake (or 'drop scone' for the Brits), they come out more cookie-like in texture.  (or biscuit-like for the Brits).

update : I should've also mentioned that many of the items that I've listed are can be served at room temp, which makes them ideal for transporting ... and while adding this, I remembered that you said 'slow carbs' ... so the potato-based ones are out.  The tortilla de patatas or the matafan could likely be made with sweet potatoes instead.  For the latkes, I'd specifically look for a recipe that calls for sweet potato, rather than trying to adapt it on your own.  And for those without the potato restriction, there's also German potato pancakes (which can be similar to latkes)