When Malachi says, "I'll drop my diskin'", what is he referring to?

"Diskin'" refers to cultivation. In context, they are preparing the cornfields. I do not, however, think this is the actual definition. Yes, the fields are being prepared but Malachai has been under the car, thus, we might infer that he was working on the brakes.

Malachai came out of the barn. He had been under the Model-A.