Kragh was born in c. 1729. His father was a farmer in northern Jutland. By 1754, Kragh served as the Danish West India Company's chief trader (overkøbmand) on Saint Thomas with an annual salary of 600 rigsdaler.[1] He was awarded the title of kammerråd. When the Danish West Indies became a crown colony, by royal resolution of 8 April 1755, he entered royal service as bookkeeper and warehouse manager on Saint Thomas. On 19 November 1755 he handed in his resignation. He was later appointed as vice commandant with title of justitsråd. On 4 December 1767, he was appointed as interim commandant of Saint Thomas and Saint John. On 10 April 1770, he was appointed as commandant of the islands. On 29 May 1770, he was appointed as infantry colonel. A few years later he became decrepit. In 1772, the civilian part of his duties as commandant were transferred to his son-in-law, Georg Hjersing Høst, with an obligation to consult wither Kragh or the governor-general in all important matters. Kragh died on 29 April 1773 on Saint Thomas.[1]
Krah was married to Elisabeth Hoffmann (née Esmith, 1711–1782).[1]
Kragh was a plantation owner. His holdings may have comprised Mary Point Plantation. This plantation was at least later owned by his son Augustus Kragh.[2]