Flounders became a JP for Shropshire. In 1813 he was one of three gentlemen nominated for appointment as High Sheriff of Shropshire but he declined on the grounds he lived permanently in Yarm and would therefore be living up to 180 miles away from Shrewsbury where the courts would be held. He appealed against similar nominations for similar reasons in 1814, 1820 and 1836.
Flounders became a Justice of the Peace (JP) for Shropshire. In 1813, he was one of three gentlemen nominated for appointment as High Sheriff of Shropshire but declined due to his permanent residence in Yarm, which would have required him to commute over 180 miles to Shrewsbury for court proceedings.