I was planning to use Haxe NME to develop a simple bluetooth chat application.
Is it possible to use device specific native APIs with Haxe? Or is there some wrapper class available to use bluetooth?
The barrier to entry to using Bluetooth protocols is fairly high and is not a commonly used method to communicate easily for a chat application cross-platform. For example see this comparison chart of frameworks not supporting bluetooth; http://www.markus-falk.com/mobile-frameworks-comparison-chart/
What is more commonly used is socket network connections, you can see a sample of a chat application with nme that works nicely cross platform https://github.com/RealyUniqueName/StablexNet
I am sure that a native extension could be written but I don't expect to see one anytime soon as its not so simple. If you want to take the challenge maybe you could look at writing an extension for http://developer.android.com/reference/android/bluetooth/BluetoothServerSocket.html
Bluetooth is more generally used with bluetooth profiles and peripherals designed for them http://en.wikipedia.org/wiki/Bluetooth_profile.