He's "a good kid" but a typical teen. A lot of 15 year olds don't want to be seen with their parents (museums, ice cream dates, sitting together in a restaurant or walking together at the mall). Some of that you let go. They're "training" to be independent adults and it's okay. But you don't take any backtalk.
At 15, learning disability or not, he's plenty old enough to understand the rules of thew world, which include not getting something for nothing. You want a paycheck? You do your assigned tasks. You want an "A" in history? You work, keep track of your own assignments, face the music with the teacher if you don't do or turn in your homework, and budget your time. You want spending money? You work. You want special privileges? You become a cooperative family member.
Stop reminding him about chores. If you feel he does better with a list, post one someplace. As soon as he nags you for a ride, for spending money, for someone to make his lunch or dinner, for XYZ favorite snacks...."Oh, did you check the job list, honey?" Don't lecture him or list all the things on the job sheet - just tell him to check it himself. You have to take the argument out of it.
Start by putting him in charge of his own laundry and his own room. Close the door to the room if you can't stand it, but he doesn't get to take food in there if he doesn't clean. He needs a clean shirt? He's perfectly capable of starting a washing machine. If he can operate a gaming control, he can operate a vacuum cleaner.
Anyone who is too immature to do the work or to remember to look at the list of things needing to be done is WAY too immature to remember, say, traffic rules when he gets a learner's permit. He doesn't need you to remind him to work - he just waits for you to get good and ticked off before he does it; he takes multiple reminders because you allow them. So let him know that anyone too young to remember basic instructions is too young to remember to call the fire department if there's a fire (therefore he can't stay home alone) or too young to be allowed at the movies alone or at the mall without supervision. But above all, STOP ARGUING! It's better for you, and it disarms the teen - he actually will start to realize that you are in charge and have the ultimate control. He can't fight you if you don't fight him. Don't wait for him to be grateful for you giving him food/clothing/shelter - just use his 'currency' which is privileges.
In my experience, it gets better at 16 or 16.5 (when driving classes loom) but it's less painful for everyone if you ease him into it now and he sees that you mean business.