is the eruv in Flatbush permissable to use?
Rav Moshe Feinstein did not approve the eruv, and maintained that the eruv would not permit carrying on Shabbos. In his wake, the majority of leading poskim do not permit the use of the eruv, and it should not be relied on. However, there are certain communities (such as disciples of Mishnah Halachos, and Klausenberg chassidim) that rely on the eruv, following the ruling of other authorities. For concrete questions of extenuating circumstances, a Rav should be consulted.
Sources: See Iggros Moshe, Orach Chaim 4:87-89; however, see Divrei Malkiel 4:3, and others, who write that an eruv can be made even for large cities (see Otzros Yerushalayim 261-280, p. 1157).