Question for readers: was this purely a tidal inlet and drainage route, or was there a real creek from a source further inland?
A local landmark was the Vanderveer Mill, also known as the Red Mill because it was painted barn-red. This was a tide mill built either in the late 1600s or sometime around 1770; I haven't yet been able to deterimine when exactly it first started operating. (It may have been that an earlier mill operated in the late 17th century, and was replaced by the better-known Red Mill around 1770). It lasted until 1879 which it burned down (According to Brooklyn by Name: How the Neighborhoods, Streets, Parks, Bridges, and More Got Their Names, By Leonard Benardo & Jennifer Weiss; NYU Press, 2006). It was built by Cornelius Van Der Veer (or Van Der Veer), or possibly his descendents. He and his descendents also owned a massive farm covering much of today's Flatbush and Canarsie, Brooklyn.
Forgotten-NY's excellent page mentioning this area:
http://www.forgotten-ny.com/NEIGHBORHOODS/canarsie/canarsie.html
and from the same page, map showing area in 1898:
http://www.forgotten-ny.com/NEIGHBORHOODS/canarsie/canarsie1898.html
From http://www.veerhuis.org/genealogy/VanDerVeer.html
He is believed to have departed Amsterdam and arrived in America on Feb 17, 1659 on the ship De Otter , taking up residence in Midwout, what is now Flatbush, NY.
On 13 Jun 1661 Cornelius was one of six persons who petitioned Gov Stuyvesant for a patent of land, who authorized a survey.
In Feb 1678 he purchased a farm in Flatbush for about 2600 guilders.
In 1683 The Assement Roll of Midwout lists him as having 100 acres.
This land became known as the 26th and 32nd ward of Brooklyn and was owned by his descendents until 1906.
The Vanderveer Park addition was the last remaining section of the original property and is located near Brooklyn College.
He and his son-in-law Daniel Polhemus, erected a grist mill on Fresh
Kill in Flatbush, later known as Vanderveer Mills, which came into the
hands of his son Dominicus, and later his grandson Cornelius.
He died in Feb, 1703 in Flatbush, NY.
(image from NYPL-- their photo/image archive also has more; if you find links to other images please post in comments.)
Map of the area:
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http://maps.google.com/maps?f=q&hl=en&geocode=&q=Williams+Ave+%26+Flatlands+Ave,+brooklyn&sll=40.651276,-73.88649&sspn=0.016801,0.040898&ie=UTF8&ll=40.646196,-73.885074&spn=0.016802,0.040898&z=15
I am not at all sure about this, but I have seen a reference to the "Canarsie Van Der Veer House" at 106 Flatlands Avenue as part of the Fresh Creek Mill, located here:
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