Per Staples p 12, Ephraim Bowen identifies a Benjamin Dunn, though this was, in all probability, actually Samuel Dunn (see State of Rhode Island and Providence Plantations at the End of the Century, A History , edited by Edward Field, Boston, Mason Publishing Co., 1902 Vol. I, p. 467-468 for the discourse on Benjamin vs. Samuel Dunn). Bowen identifies Dunn as one of the sea captains assigned to command one of the longboats that, together with seven other such boats, attacked the Gaspee in 1772:

....and a sea captain acted as steersman of each boat, of whom I recollect Capt. Abraham Whipple, Capt. John B. Hopkins, (with whom I embarked,) and Capt. Samuel Dunn. A line from right to left was soon formed, with Capt. Whipple on the right and Capt. Hopkins on the right of the left wing.

According to Field, Edward, State of Rhode Island and Providence Plantations at the End of the Century:  A History.  Boston, Mason Publishing Co. 1902, Vol II, p424 Samuel Dunn, Jr. served as master, then owner, of the privateersman Revenge in 1776.  We have discovered that there were several Samuel Dunns in America at the time, several who had served in the Revolution, notably from Virginia, New York, and New Jersey.  There was also a Samuel Dunn from Providence who married an Esther Tourtellot and had several children, including a Samuel Dunn, Jr. born in 1747.   And there was a Samuel Dunn from Newport who had children with a Sarah Bailey in the 1720s. This all may create some genealogical confusion.

• There was a Samuel Dunn who served under Commodore Perry in the Lake Eire Battles of the War of 1812 <http://ftp.rootsweb.com/pub/usgenweb/oh/newspapers/war1812/w1812v-b.txt >
• and there was a Captain Samuel Dunn who led a militia company from Cape Elizabeth, Maine in 1775 <http://ftp.rootsweb.com/pub/usgenweb/me/cumberland/capeelizabeth/company/must1775.txt >
• and a Lieutenant Samuel Dunn on the rolls of the 1793 New Jersey state militia census with the 1st Company of Grenadiers < http://freepages.genealogy.rootsweb.com/~zenasriggs/Military/1793newtongren.htm > (Stale link 2005) This latter case would have been a demotion, however.

Mrs. Kate S. Baldwin Andrews.
DAR ID Number: 49568
Born in Nashua, N. H.
Wife of Frank A. Andrews.
Descendant of Capt. Samuel Dunn, of Rhode Island.
Daughter of Josephus Baldwin and Lucy Stone, his 2nd wife.
Granddaughter of Daniel Stone and Mary Ann Cole, his wife.
Gr-granddaughter of Thomas Cole and Desire Dunn, his wife.
Gr-gr-granddaughter of Samuel Dunn, Jr., and Lucy Pierce, his wife.
Gr-gr-gr-granddaughter of Samuel Dunn and Priscilla Ball, his wife.
[p.250] Samuel Dunn (1710-87) was captain in the Continental army and assisted in blowing up the British ship “Gaspee,” off Gaspee Point, which was one of the events leading up to the Revolution. He was born and died in New Shoreham, R. I.

The American family of DUNN traces its ancestry to Capt. Richard DUNN, a descendant of Robert DE DUNN, Lord of Breadsall, temp. Henry I, 1100-1135, who came from England to America about the middle of the 17th century and who settled at Newport, R. I., in 1647, and d. circa 1712. He was a Deputy to the Colonial Legislature in 1681, 1705, 1707-8, -9 and -11. He held the rank of Lieutenant and Captain in the “Train Band,” of the Colonial Forces of the Colony. m. (name unknown).

I. Richard, b. circa 1669.
II. Samuel, b. circa 1670.
III. NATHANIEL, b. 1671; d. 28th Feb. 1735, at New Shoreham, R. I.
NATHANIEL DUNN, b. 1671; d. 28th Feb. 1735; m. Elizabeth LAWTON, dau. of Daniel LAWTON of Portsmouth, R. I.
I. SAMUEL.
 CAPT. SAMUEL DUNN, b. circa 1710; d. 1790. Commanded one of the three boats that captured and destroyed H. B. M. ship “Gaspee,” 9th June, 1772, in the Providence river and shot Lieut. DODDINGTON, R. N., the commander. In 1740 he went with Admiral VERNON on the attack on Carthagena, Columbia, S. A., as a Captain of a company of the Colonial troops of Rhode Island. m. 15th Oct. 1730, Priscilla BALL of New Shoreham, dau. of John BALL.
I. SAMUEL, Jr., b. 3d Jan. 1743.
[p.237] CAPTAIN SAMUEL DUNN, Jr., b. 3d Jan. 1743; d. 15th Dec. 1787. Commanded and afterwards owned the celebrated privateer “Revenge,” also “Prosper,” during the War of the American Revolution, sailing mostly from Newport, R. I.; m. 12th Sept. 1773, Lucy PEIRCE, dau. of Giles PEIRCE, Jr.
I. JOHN, b. 3d Dec. 1774.

There's no Priscilla Dunn in the cemetery records, and we can't find offspring data other than the reference to Samuel Dunn, Jr. of 1743.

No Dunn or Dunne family shows up in the 1770 List of Providence taxpayers. This could be expected, since he lived his home life on Block Island.  It appears, that Captain Samuel Dunn is almost unique amongst his fellow Gaspee raiders in not being related to others by blood.  It is more probable, however, that he was connected by the nature of his employment.  As a sea captain, one might surmise that he operated a packet service between Block Island and Providence, probably had been personally harassed by the Gaspee, and happened to be in the town of Providence on the night when the opportunity arose to rid Rhode Island of the British menace.

1. There were multiple Samuel Dunns in Rhode Island at this time, and the page as it is certainly conflates them.  For instance, you mention the death notice of Samuel Dunn in 1790 at age 66 and notes that the birth year would then be off by quite a lot from 1710.  That's because the Samuel Dunn of the New Shoreham branch of the Dunn family was born in 1710, but the Samuel Dunn of the Newport branch was born in 1724.  The latter Samuel Dunn married Esther Tourtellot.  These were the mother of Anne who married future Rhode Island governor William Jones and of Esther who was grandmother to future governor Elisha Dyer.

2. There was a Benjamin Dunn who lived at this time in Rhode Island, although he does not appear in the Rhode Island Cemetery Commission database.  Chapin states that Benjamin Dunn b. 13 July 1749 was the brother of Samuel Dunn b. 1724.  The manuscript claims that a separate manuscript by William Jones Hoppin (which seems likely to be with Hoppins's papers held at the Rhode Island Historical Society) claims that this Benjamin participated in the Gaspee Affair.  Chapin's manuscript states that this Benjamin died in an engagement with a privateer on 9 January 1779, so perhaps it is not surprising that his grave cannot be found.  Would it not also be reasonable that multiple Dunns joined in the attack, especially if they were brothers or cousins and were together when the news of the Gaspee's vulnerability reached them?

3. In spite of the accounts that say the Samuel Dunn involved in the Gaspee Affair was the same who participated in the Cartagena Campaign of 1740-1741, this seems highly unlikely.  The Samuel who captained the Newport Company of militia was most likely Samuel b.1699 father of Samuel b.1724.  Chapin quotes from a family bible belonging to the younger Samuel in which he wrote "my honored father commander of one of His Majesty's companeys on foot against Cartagena died in Jamaica 1740 in the 42nd year of his age". 

This is clearly written by Samuel Jr., who would have been 16 years old at this time and clearly would have known the reason for his father's disappearance.  This account is wholly consistent with Samuel Sr. having died during staging for the operation.  The Rhode Island militias arrived in Jamaica in December, only to find themselves poorly provisioned and having to wait for the bulk of the British fleet.  During the next couple of months, disease decimated the American militias.  Disease continued to take a toll once the operation against Carthagena commenced in March, and there is a report that "no more than 20" Rhode Islanders returned from their group.

4. The most reasonable candidates for Samuel who participated in the attack are then (A) Samuel of New Shoreham (1710-??) son of Nathaniel; (B) Samuel Jr. (1743-??) son of (A); (C) Samuel (1724-1790) son of Samuel and first cousin once-removed to Samuel (A); (D) Samuel Jr. (1747-1815) son of Samuel (C)