How can I paint a dark gray wall to make it look like barnwood?

Yes, it depends on how much like wood you want it to look. You will need brown and white glaze to achieve this look. Glaze is a special kind of paint that dries slow and you can paint on and wipe up what you don't like. You would paint on a little brown and white glaze - varying it to give it the color you like over the gray. Then you'll use a wood graining tool to pull the glaze off and give it the wood grain look. If you don't like the way it looks you simply wipe it up and try again. Work in small sections. You can see a table I did here with the tool - https://chascrazycreations.com/faux-wood-grain-table/

If you mean streaks you. Outdoor take a whisk broom and jently go across after you paint

I have a tutorial on getting the barnwood looking finish. I used it on furniture, but the same paint and techniques could certainly be used on a wall! https://www.hometalk.com/diy/living-room/furniture/diy-faux-barn-wood-finish-38036616?r=2

DIY Faux Barn Wood Finish