From the book Nelson Barbour: The Millennium's Forgotten Prophet (available at lulu.com) :
Barbour and his associates did not immediately reconsider Gentile Times. The issues of an invisible parousia and other chronological speculations came first. We also do not know who among them initiated the discussion. In the absence of other claims, it is probably safe to suppose that Barbour was responsible for concluding Gentile Times ended not in the 1870s, but in 1914. The first mention of the 1914 date as the end of The Times of the Gentiles is in the September 1875 issue of The Herald of the Morning. In passing Barbour remarked, “The time of the Gentiles,” viz. Their seven prophetic times of 2520 years ... which began when God gave all into the hands of Nebuchadnezzar, in 606 B. C; do not end until 1914.
Barbour is indebted to John Aquila Brown for the 2520 year computation. Brown in turn owes the calculation of the “seven times” of Daniel’s prophecy as 2520 years and the association of it to The Times of the Gentiles to Joshua Spalding.
Spaulding wrote Divine Theory; A System of Divinity in 1798, though it seems not to have been published until 1808. Spalding, writing of the seven-times of Daniel’s Great Tree Vision, said:
Seven times, or one full week of years, upon the great prophetic scale, is 2520 years. This supposition is much strengthened by the consideration, that the continuance of mystical Babylon is said expressly to be for a time, times, and a half; and as the times allotted for this division of the empire, is the half of a week, three times and a half, it is natural to conclude, that the whole of the times, called the times of the Gentiles, is a whole week, or seven times.
Though Spalding was an American clergyman, the British Library Catalogue testifies that his books circulated in Britain . It is possible that J. A. Brown was familiar with Spalding. Yet it seems certain that Brown played a part in influencing Barbour that Spalding did not.
That Gentile Times were 2520 years became a standard view among expositors. The popularization of the 2520 year calculation was probably due to George Stanley Faber. He used the calculation in The Sacred Calendar of Prophecy, published in 1828.
When The Christian Guardian and Church of England Magazine reviewed Faber’s book in 1830, it accepted without question the 2520 day calculation, though it suggested Faber had no basis for his start date. Edward Bickersteth adopted the calculation in the mid-1830s. His reputation as a pious Bible scholar sealed it into Advent thinking.
If the 2520 year calculation isn’t original to Barbour, nothing else in his ‘“Gentile Times” calculation belongs to him either. Faber mentioned the 606 B.C. date in his 1811 work A Dissertation on the Prophecy Contained in Daniel ix, 24-27 .
In the 1820’s, several authors pointed to 606 B.C. as the date at which the seventy-year long exile began. In 1834 Matthew Habershon mentioned the 606 B.C. date, but calculated the “seven times” from three years later, ending them in 1918.
William Miller adopted the 2520 year calculation but ended it in 1843. John Dowling, a Baptist pastor, criticized William Miller’s method for calculating the “seven times,” suggesting that " it would have answered the purpose ... much better had this subtraction happened to have brought out the number 606 B.C., the date of the commencement of the 70 years captivity of the Israelites in Babylon ."
It seems certain that the ultimate source for Barbour’s 1914 calculation is E. B. Elliott’s Horae Apocalypticae, where the 606 B.C. to 1914 calculation is found.
The next mention of the 1914 date in connection to “Gentile Times” I can find is by an anonymous author writing in The Original Session Magazine in 1850. The magazine was published in Scotland but saw circulation in the United States . This author suggested that the “seven times” would end in 1897, yet his calculation took him to 1914. He arrives at his other dates, including the 1897 date by a complicated series of additions and subtractions from the basic “2520 - 606 = 1914” calculation. If one removes all the puzzling additions and subtractions, one has Barbour’s usage. There is no way to know if Barbour was familiar with the Session magazine but he almost certainly was familiar with John Dowling and Habershon, and he tells us he read Elliott’s Horae Apocalypticae.
It is worth noting that Samuel Davies Baldwin taught that the actual date was 607 B.C. He dated the seventy years from 607- 537 B.C., a view later adopted by Jehovah’s Witnesses.
Baldwin, S. D.: Armageddon: Or the Overthrow of Romanism and Monarchy’ The Existence of the United States Foretold in the Bible, Its Future Greatness; Invasion by Allied Europe; Annihilation of Monarchy; Expansion into the Millennial Republic, and its Dominion over the Whole World , Applegate and Company, Cincinnati, 1863, page 424.