Leak really fixed?
Yep, that is my goal, not going for a quick fix here. Previously water was getting into the window above this crack cause it was pouring over the edge of a clogged gutter. That's been fixed. No more water in the window sill. Problem is I still see this flaking off.
The flaking problem is local to under the window only, which makes me think it is window related. Only other thing I can think of is that the window isn't flashed properly, which I'll check into when it warms up.
gjones8131, you say you fixed the leak by making sure that water stopped pouring over the edge of a clogged gutter? You may have stopped water from flowing over the gutter and down into your house, but it doesn't sound like you fixed the leak where the water was getting through your window and into your exterior wall. A driving rain might also get water into the leak that is still there. The water pouring over the gutter wasn't the leak, it was just a source of water that pointed out the leak. It seems to me that you still have a leak where a driving rain can still cause damage.
I agree with those that feel you need to make sure that the affected area is properly dried out before you attempt repairs to the wall. My concern about residual moisture is whether it is causing any mold growth. If there is still an avenue for water to leak into your house, this avenue might also allow moisture to constantly move into the wall.
If you find that you have mold growth inside the wall you might have to think about how to treat the mold. One possibility is to spray a product called Concrobium into the outlet hole using a fogging machine so it will saturate all the surfaces it comes in contact with. Concrobium is sold at Home Depot. Home Depot also rents a fogging machine to fog the Concrobium.
I was thinking that if you temporarily removed the wall socket and hooked up a wet vac exhaust to the hole, the warm and dry interior air (amplified by the wet vac to be hotter) might push enough dry air into the area to dry it out faster than leaving it to do so gradually. I would also scout around outside the window to find where the water came in - and may still come in during a driving rain!
When the area is dry enough to repair, I would scrape away as much loose material off of the grayish material in the photo. I would then coat this grayish material with 2 or 3 good coats of Gardz sealer (originally designed as a concrete sealer) and let dry thoroughly between each coat. The Gardz will soak in and solidify any loose material and give a good base for spackling.
I would then skim the coated area with USG Durabond 20. USG also makes a product called Easy Sand. If you dropped a clump of Easy Sand on a concrete floor and let it dry, you can come back and slice it off with your mud knife. If you try to do the same thing with a clump of Durabond, you might damage your mud knife! Durabond sticks like crazy to most surfaces. I would put 2 or 3 coats of Durabond on, taking care not to build up the Durabond, but keeping it as flush to the wall as possible. When each coat dries, all you should have to do is take your mud knife and scrape/slice off any lines or nubs, then skim again. The idea of doing it this way is so you have minimal Durabond build up to sand. I have gotten surfaces smoother than a baby's a__ doing it this way. When the patched area is smooth enough to paint, I would sand lightly, then apply another good coat of Gardz, let dry thoroughly, then paint. If you don't want to buy a large bag of Durabond you could probably buy a small container of USG's Green Top mud. Be careful not to overfill this as it is also difficult to sand.
Without being there and seeing things for myself, this is how I might do it.