What area of LA cuz it really does matter? Coastal, inland, valleys, mtns?
Pick up a Sunset Western Garden Book and learn your Sunset zone on what you can and can't plant. The stores will carry anything people ask for but it may not grow in your specific area.
Don't plant anything until at least Oct. It's too hot now to start anything.
Creeping fig should cover the block wall and anything else in its path. Plant it about 5 feet apart.You'll have to water anything to get it going and if you are inland it might need some water in Aug-sept.
Put in more jasmine in front. It might be slow to get it started but it will cover the fence.

I am in Pasadena and I think I am in zone 9B.

Should I hold off on planting vines on my concrete wall, even though the entire wall is shaded under a tree? I have more time to water this summer.

Check out the variety of passion vines. Some even give fruit.

They will get a much better start in Oct.

In youthful innocence I planted a 1 gallon creeping fig (Ficus repens) on a 30ft. length of cinderblock fence. I lived to regret it. Within 7 years!

Then I planted 1 gal. Boston ivy (Parthenocissus tricuspidata) and loved it even tho it dropped its leaves in the winter (dug them in). The winter tracery on the fence was nice and so fun to see spring leaves. Almost as if we were having seasons in the southland. Easy to control. Rose bushes in front were watered but no extra needed for the vine after the first year. I'm glad I used only 1 plant. It spread well after a couple of years.

I learned about concrete nails a few years later. So could have used something non-clinging. However I was pleased with the Parthenocissus. Being deciduous it never became the rank mess that is common with many vines. No home for vermin there. I doubt the oak shade would be a problem.

Creeping fig will cover a cinder block wall and soften it nicely. It's good in that it will attach itself to the wall and you won't have to tie it up to support it, it won't take up a lot of space like a hedge will, it's not picky about soil, and doesn't need water once it's established. However, it can be aggressive and produce fruit once it gets big. Regular trims should keep it in line. I've tried Boston ivy several times, but I could never get it to take off. I would avoid English ivy entirely as all it seems to do is provide cover for unsavory creatures you'd rather not have around. For a vine that requires support, I'd recommend vitis Californica "Roger's Red", a native grape vine that provides beautiful reliable fall color.