As long as both plans are HSA-eligible, there are no issues, and you can contribute to your full limit for the year. Having two HSA-eligible HDHPs is not considered "other coverage" that would disqualify you.
Additionally, qualification is determined on the first day of each month, which means that since the first plan will end August 31, you would not have overlapping coverage on Sept 1 even if the overlapping coverage from 8/25-8/31 was disqualifying (which it is not)
