Non-lawyers do not realize how complicated the First Amendment is. In this case, the State of New York conveyed to the City of New Rochelle the Armory, which had to remain open for public use. The City then allowed a local veterans' group to display and maintain flags at the Armory. The groups wanted to run a "Don't Tread on Me" flag up the pole, but the City made them take it down. Do the veterans have a case? They do not.
The case is United Veterans Memorial v. City of New Rochelle, a summary order decided on September 9. Flags are pure speech, and the flag in this case, formally known as the Gadsden Flag but known to us these days as the Tea Party flag, promoted a particular political message. Here's a picture of the flag for you to ponder. Can't the veterans fly this flag? Under normal circumstances they can, but in this case, they cannot.
Under the government-speech doctrine, the government can promote a message on its property without having to afford equal time or other speech opportunities to citizens. This doctrine gained attention a few years ago in the Pleasant Grove v. Summum case, where the Supreme Court said the government was not required to post a private organization's religious monument in a public park, which had already contained 15 permanent monuments, including a 10 Commandments monument. Since we're talking government speech in the Summum case, the property was not a public forum, which requires the government to allow people to express themselves freely.
Summum controls the New Rochelle case. The Armory is a government building. As the district court held, and the Second Circuit affirmed, "it is not plausible that a reasonable observer would consider the Gadsden Flag flying at the Armory to be private speech, and it is obvious that the flag would be regarded as government speech. ... The Armory and its flagpole are owned by the City, and flags, like monuments, are reasonably interpreted as conveying a message on the property owner's behalf." The Court of Appeals holds that "the City was well within its rights to delegate to United Veterans the right to display and maintain flags on the City-owned flagpole without creating a public forum of any sort, or relinquishing control of the flags displayed."