The Intercept has leaked and analysed the guidelines the US government uses to place people on its "no-fly" list. Its a long and detailed article (the Guardian has a shorter summary here) and it shows just how arbitrary and baseless the list is.
The basic standard of evidence by which the US denies its citizens the right to travel is "reasonable suspicion" of connection to "terrorism" (which is defined broadly to include property damage and pressuring governments). What's "reasonable suspicion"? Anything they damn well like. Tweets, gait analysis ("he was walking like a terrorist!"), going on Hajj, getting married outside the US, travelling for "no reason" (meaning: acting like a citizen of a free country and not telling the government what you're doing every day of your life), being related to someone they classify as a "terrorist", being a potential informant for the FBI, refusing to be an informant for the FBI. And even that low threshold can be bypassed if they feel like it. As they say, "concrete facts are not necessary". And the result is predictable: they added 468,749 people to the list last year, up from 227,932 in 2009. So there are probably millions of people affected. And there's no formal process for removing the innocent...
The US apparently shares this list with 22 other governments. New Zealand is almost certainly one of them. I'm not aware yet of any kiwi being forbidden to fly by unaccountable US officials, but its probably only a matter of time.