The son of Sir Henry Fletcher, Bt and Catharine Dalston, he succeeded to his father's baronetcy in 1645. Between 1657 and 1658, and between 1679 and 1680, he was Sheriff of Cumberland. Fletcher was Member of Parliament (MP) for Cumberland from 1661 to 1679, from 1681 to 1685 and from 1689 to 1700.
On 27 February 1654 or 1655, he married firstly Alice Hare, daughter of the 1st Baron Coleraine in Totteridge in Hertfordshire. Fletcher married secondly Lady Mary Johnstone, daughter of the 1st Earl of Hartfell c. 1655. He had one daughter and one son Henry Fletcher by his first wife.