Amy Duggar King has gotten pretty close with her cousin Jill Duggar Dillard ... especially in the wake of Joseph Duggar 's arrest. In a new YouTube chat with interviewer Dory Jackson ... Amy says she and Jill -- who's one of Joseph and Josh Duggar 's sisters -- have been texting a ton since Joseph was arrested in March for allegedly sexually abusing a minor in Florida. Amy said ... "We have definitely sent messages back and forth, all week long, you know, for weeks now of just like, 'Are you