Your post is a little confusing (June 10th has way passed). When do you plan to leave your losing unit? That is where you need to start and account for the amount of leave days you want to take. Remember to have the required days available.
When you are authorized early report, and you want to report on that day, your DA 31 should end on that early report day.
If early report is August 10th, then that is the first day Benning is expecting you. So, if my normal report date is September 10th but want to take 30 days to the early report date, then my leave will be from July 11 to August 10th. If you are authorized 10 days permissive TDY, then you can start that on August 10th and you will check-in on August 20th.
But if you want to check in immediately after you start leave, just realize that your leave will stop at that time and you will begin to in-process. If you want to take leave after checking-in, then you will have to wait to you are assigned to your gaining unit to get it approved but then you might run into issues of getting it approved.
Remember, ever though you are allowed to early report, does not mean you have to.