Should I get a thin, flat bottomed wok to stir fry large amounts of veggies on an electric stove?
I'll try address your questions:


Firstly, woks should always be thin. The point of a wok is to get extremely hot at the bottom, without heat being conducted much up the sides. Thin is best for this
The problem with this in your case, is that a small amount of your vegetables will be touching the bottom and cooking, while most will be sitting on top, or in contact with the sides, just getting warmed slightly.
The point of a stir fry is to slightly char the vegetables as they get tossed around the pan, moving between hot and cooler parts, so that they cook evenly, but get a good browning at the same time. The problem is that this is really only suited to smallish amounts of food, unless you have an enormous wok and burner/stove.
As you have indiciated that convenience is more important to you than flavour/cooking quality, I would suggest a large, flat, heavy bottomed frying pan (fine with straight or curved sides). This will cook large amounts of veg best, without cooling down too much when you add them, and the larger bottom surface will mean more veg is getting contact with the hottest surface


I wouldn't normally recommend a plain frying pan for stir fries, but I think this is the best option in your case. The outcome will not be the same as a stir fry - might be more moist and less browned, but should suffice for convenience's sake