Simple Answer: No, there is no evidence Arnold ever regretted his decision.

Long Answer: Traditionally, Benedict Arnold is portrayed by most American Revolutionary historians as one of Washington's most promising commanders whose flip to the British was entirely unjustified. He was a stubborn man who rarely second guessed himself and even rarer ever admitted when he was wrong. Now, I am not going to counter this narrative, however it is worth noting the reasons he himself gave for the flip as well as understanding what his life was like prior to his turn. Much of my information on this is being taken from James Kirby Martin's Benedict Arnold, Revolutionary Hero: An American Warrior Reconsidered which is a highly respected volume on this character. Here, Martin easily explains that in the time leading up to his treasonous ploy, Arnold felt betrayed wholeheartedly by the fathers of the American Revolution. After having the successes of his own achievements stolen by rival officers in Washington's Army time and again, and after being felt numerous insults by the Continental Congress and even Washington himself, he felt that he deserved better, and as such he decided to flip sides in exchange for a commission as a Brigadier General in the British Army.

After a short stinted campaign that stretched from Virginia to New York, Arnold would eventually leave for England in December 1781 when the war was all but over. Arnold would attempt to convince British lawmakers to continue the war, but to no avail. Soon thereafter, the war was declared over and Arnold was frail, highly in debt, and in search of trying to restore his family’s good name in England (which his father had squandered away due to alcoholism when Arnold was a child). However, very little regret in choosing the British appears to be on his mind as Arnold continued on with his life.

Barry Wilson's biography, Benedict Arnold: A Traitor in Our Midst actually outlines some important facets of Arnold's life that are often over-looked by historians because for most studying the man, the interest in studying him ends with the conclusion of the war. Wilson continues on with Arnold's life all the way until its conclusion. Here we learn that between 1785 -- 1800, Arnold bounced around various shipping and business ventures as he tried to right his family's name and get them out of debt, and eventually situated himself in Canada, where he remained until shortly before his death. Suffering from gout, he was highly mobile and frail and he continued to struggle financially. He would die in August of 1801 and his death was mostly unnoticed by the people of Great Britain, with newspapers barely making any type of a fuss about it, such as New Brunswick's Royal Gazette which simply stated on page 3, "Died in England, Brigadier General Benedict Arnold, late of this city."[Wilson, pp 227). As Wilson himself easily summarizes the end of his life:

That was it. No obituary, no mention of his remarkable past, his accomplishments and heroics, his flaws, his dealings in the city, his notoriety. His death rated just the telling, without embellishment. It was fitting. Arnold, in his last years in London, received few kudos. He associated with some members of the elite, was consulted by the King, and carried on business. He also slid deeper into debt and ill-health... The British government promised, and then retracted for budget reasons, compensation for past expenses incurred but never covered. [Wilson, pp 227-228]

Indeed, the end of Arnold's life is a sad tale, yet he did not appear to regret his decision to defect to the British cause. His wife, whom he appeared to love dearly, was there to the very end and her many letters to family, including their sons, never hinted that Arnold wished he would have sided with America during the war. The problem though is that some early American historians (most from over a century ago) actually have contrived a fictionalized ending to Arnold's life, one where he was laying out his old Continental Army uniform and saying how he never should have done such a thing, however there is no evidence of this. "As a man not known for second-guessing himself, the story does not emit the scent of truth but rather the tarnish of propaganda masquerading as history." [p228]

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Follow up: What were his reasons for siding with the British?

Was the war thought impossible?