Use water or milk to thin the eggs, and not oil. I've found the eggs by themselves were too thick and didn't stick well, but thinning them out let them wet the surface evenly enough to get breadcrumbs sticking nicely.
And oil won't help any of it stick, and doubly so because the oil will probably make it easier for the coating to dissolve in the cooking oil, rather than staying together. Besides, you will likely get enough oil in the recipe from frying.
As for flour... well, I've used it sometimes, and not used it sometimes, I've never seen a dramatic effect from pre-flouring before an egg wash, at least not one that outweighs the extra fussiness of the step. On the other hand, I sometimes make a thin batter with flour, spices and the egg mix, and dip in that before the breadcrumbs for a thicker crust... which is probably a similar effect to a flour layer, but much easier for me.
Disclaimer - I've used these breading techniques on cheese, or on vegetables like eggplant, and not actually on chicken - I think the principles would be similar, though.