How can I determine if iPhone is set for 12 hour or 24 hour time display?

Here’s the best way to do it:

NSString *formatStringForHours = [NSDateFormatter dateFormatFromTemplate:@"j" options:0 locale:[NSLocale currentLocale]];

NSRange containsA = [formatStringForHours rangeOfString:@"a"];
BOOL hasAMPM = containsA.location != NSNotFound;

in Swift:

let formatString: NSString = NSDateFormatter.dateFormatFromTemplate("j", options: 0, locale: NSLocale.currentLocale())!
let hasAMPM = formatString.containsString("a")

Swift 4:

let formatString = DateFormatter.dateFormat(fromTemplate: "j", options: 0, locale: Locale.current)!
let hasAMPM = formatString.contains("a")

This uses a special date template string called “j”. According to the ICU Spec, “j”…

requests the preferred hour format for the locale (h, H, K, or k), as determined by whether h, H, K, or k is used in the standard short time format for the locale. In the implementation of such an API, ‘j’ must be replaced by h, H, K, or k before beginning a match against availableFormats data. Note that use of ‘j’ in a skeleton passed to an API is the only way to have a skeleton request a locale’s preferred time cycle type (12-hour or 24-hour).

That last sentence is important. It “is the only way to have a skeleton request a locale’s preferred time cycle type”. Since NSDateFormatter and NSCalendar are built on the ICU library, the same holds true here.