There were criminals of Dutch and English descent, but mafias in the US are typically associations of minorities with some recent history of immigration and alienated from authorities. People of English and the Dutch descent in North America weren't that; they were the elites, or the same ethnicity as the elites. People who feel that "the law" is on their side are less likely to find advantage in taking it into their own hands. If your uncle is the Mayor, you don't need to go rogue.
So while there was criminality -- there always is-- it generally wasn't a self conscious ethnic affiliation. If you look at, say, Jesse and Frank James, ethnically Anglo, but there's no consciousness of an "Anglo mafia" in their case. Similarly Bonnie Parker and Clyde Barrow are just criminals. When there's a criminal conspiracy of elites-- well, then its not considered "organized crime" in a mafia sense, it's more along the lines of official corruption. So "Teapot Dome" is how oilmen struck deals with the "Ohio Gang" -- President Harding and his cronies-- and made off with the loot. They're all Anglo, but no one calls it a "mafia"; you can if you'd like.
A dominant ethnicity is under less pressure to organize extralegally, or to have their self help organizations characterized as illegal-- the police _are_ their "gang". If you look at the way that business owners used the Pinkerton's in the 19th century, you can see that the establishment had less reason to pursue extralegal strategies-- they could get what they wanted legally. So the Irish miners -- the violence of the "Molly Maguires" was considered criminal and terroristic; while their adversary Franklin Gowen hired the Pinkerton's and got some added muscle from a rival Welsh group, the Modocs . . . that's the violence of the owners, and it rarely gets characterized as criminal.
In other places, though, where Protestants might define themselves by their differentness from newly arrived Irish catholics, you did see Anglo identifying organized crime. The Bowery Boys of 19th century New York would qualify as an Anglo gang; they identified as native and Protestant in contrast to new Irish Catholic immigrants. Similarly, the Ku Klux Klan could be described as an Anglo mafia. They don't have the commercial motivations that typically characterize a mafia-- but they are organized to commit acts of violence and their Anglo Protestant ethnicity is a defining characteristic of their membership.
With respect to people of Dutch ancestry, there weren't a lot of places where there'd have been enough people who identified with that ancestry and who were disenfranchised to form a gang. The Hudson valley had lots of old Dutch families, but they were typically "society" rather than "underclass"; they had lots of ways to get what they wanted without forming a gang. Donna Merwick has done a terrific job analyzing 17th century court cases in Albany, New York for evidence of tensions between Dutch and their new English rulers. She finds a number of incidents, but there's nothing like a "Dutch mafia" -- more just random run ins between Dutch youth and English, likely lubricated by alcohol, but against a background of assimilation. So she finds that while Dutch and English might brawl, the same people might also be doing business with each other-- very different from the ethnic segregation of business affairs that characterizes ethnic mafias.
See:
Anbinder, Tyler. “‘Boss’ Tweed: Nativist.” Journal of the Early Republic, vol. 15, no. 1, 1995, pp. 109–116.
THE BOWERY BOYS: Street Comer Radicals and the Politics of Rebellion. By Peter Adams. Westport, CT: Praeger. 2005
GREENBERG, DOUGLAS. “Patterns of Criminal Prosecution in Eighteenth-Century New York.” New York History, vol. 56, no. 2, 1975, pp. 132–153.
Weiss, Robert. “THE EMERGENCE AND TRANSFORMATION OF PRIVATE DETECTIVE INDUSTRIAL POLICING IN THE UNITED STATES, 1850-1940.” Crime and Social Justice, no. 9, 1978, pp. 35–48.
Laton McCartney. "The Teapot Dome Scandal: How Big Oil Bought the Harding White House and Tried to Steal the Country" (Penguin:2009) [not an academic work, but an entertaining treatment . . . more or less straight narrative history]
MERWICK, DONNA. “Becoming English: Anglo-Dutch Conflict in the 1670s in Albany, New York.” New York History, vol. 62, no. 4, 1981, pp. 389–414.