Just wanted to offer a correction: Apple headphones and the Apple Lightning to 3.5 mm AUX Adapter do not contain DACs. The DAC is a custom-built Cirrus Logic DAC inside the iPhone that can technically handle 24-bit Integer / 96kHz conversion, but iOS limits this to 48kHz. Without a separate app, you cannot store or play files above 48kHz. You can, oddly enough, store 32-bit Floating Point IEEE files on the iPhone though.
They have simply re-routed the electrodes that connected the former auxiliary jack to the lightning connector. The sound quality is EXACTLY the same. It ticks me off when Apple themselves claims it to be an audible improvement when it can be scientifically proven to not be the case.
The only way you can use an external DAC is via Lightning to USB, rarely built into headphone cables, and usually not as good of quality as the one built-in to the iPhone, believe it or not. The Audeze may be an exception, but I'm skeptical of its DAC actually being better than the iPhone as far as sound quality is concerned.
BTW, you may want to watch some of the videos regarding the PONO Player. It seems like a scam to a true audiophile, and even if you're not a true audiophile (whatever the heck a "true audiophile" may be), it's still vastly overpriced. I don't own one, however, so if you know something I don't, let me know.
If you want to listen to high-fidelity music on the go, just downsample your music to 24-bit Integer / 48kHz or 44.1kHz, you will lose no audible quality if you do the conversion correctly, you'll decrease the file size, and it can then be played natively on the iPhone. For the best ALAC conversion, do not use Audacity or XLD or Foobar2000, use either Adobe Audition on Mac ONLY, iTunes, or Apple's ProLogicX. I'm an audio engineer, I kind of know what I'm talking about.
P.S. If you want to convert a file to ALAC in iTunes, try to already have the file be in 24-bit or 32-bit Integer, 32-bit Float files get converted to 16-bit Integer (CD-quality). You cannot hear above 22050 Hz. A file with a sampling rate of 44.1kHz has an audible range half that number, so 44.1kHz sample = 22.050kHz audible. Beyond that, you're simply storing more data that is virtually useless. The better factor is actually bit depth, so 16-bit vs 24-bit and so on. 16-bit provides 96 dB, 24-bit provides 144, and beyond that is again virtually useless for music. If you downsample your music correctly, 24-bit Integer/44.1kHz is all you need.