You need to give him more food, 2 tablespoon a night is not enough. There should always be food in his cage so that he can eat all he wants. Don't worry he's not going to die from eating too much. You shouldn't give him dandilion leaves, it's not very popular among treats so i infer that it's not as safe. And all the treats that you are giving him, give him at most once a day. If you are using treats to train him, i recommend using rolled oats, the plain one. Chinchilla digest oat better than the other treats, and oat is small so you can give him a lot throughout the day instead of one big treat.
And about his fur, how often do you let him take bath? He should be taking dust bath 2-4 times a week. Dust bath is important to keep his fur healthy, shiny and smooth. That's the only reason i could think of for his fur problem, or it could be that he is priming like starleomach said, just use a brush to brush him off.