How do you read /dev/tty.iap on iOS?
No, you can't read /dev/tty.iap file on an iOS device. At least as long as the device isn't jailbroken.

3rd party iOS apps are sandboxed and not allowed to read the device filesystem.

From File System Programming Guide:


  The iOS file system is geared toward apps running on their own. To keep the system simple, users of iOS devices do not have direct access to the file system and apps are expected to follow this convention.
  
  
  




Unofficially speaking, iOS however allows read-only access to some parts of the filesystem as noted in this reddit thread:


  Hello everyone, I’m an aspiring security researcher, and got bored. I decided to look at how far the sandbox really lets you go in terms of accessing parts of the filesystem that aren’t part of its designated container.
  
  PLEASE NOTE: In NO WAY does this at all allow you to modify, add, or delete ANY files in the areas I am about to talk about. These areas in the system are, in UNIX terms, “Read-only”.
  
  Which directories can you view?
  
  After combing the filesystem using an app I’ll mention later, these are the directories.
  
  
  /System/Library
  /usr/lib
  /Developer
  


The above explains, why you are able to read /Developer and can't read /dev/tty.iap.