Update:

Here's the full script I'm using for displaying the device camera feed on a UI image with correct orientation and ratio, front and back cameras, and mirroring the front camera to make it look more natural, along with a screenshot of my $$anonymous$$erarchy and RawImage game object. It's based on t$$anonymous$$s answer by @Fattie, t$$anonymous$$s other answer by Max Bot, reading the Unity documentation on WebCamTexture and WebCamDevice, and trial and error on a Nexus 5 running Android 6 and an iPhone 5S running iOS 9.

Hierarchy:

DeviceCameraController.cs:

 using UnityEngine;
 using UnityEngine.UI;
 using System.Linq;
 using System.Collections;
 
 public class DeviceCameraController : MonoBehaviour
 {
     public RawImage image;
     public RectTransform imageParent;
     public AspectRatioFitter imageFitter;
 
     // Device cameras
     WebCamDevice frontCameraDevice;
     WebCamDevice backCameraDevice;
     WebCamDevice activeCameraDevice;
 
     WebCamTexture frontCameraTexture;
     WebCamTexture backCameraTexture;
     WebCamTexture activeCameraTexture;
 
     // Image rotation
     Vector3 rotationVector = new Vector3(0f, 0f, 0f);
 
     // Image uvRect
     Rect defaultRect = new Rect(0f, 0f, 1f, 1f);
     Rect fixedRect = new Rect(0f, 1f, 1f, -1f);
 
     // Image Parent's scale
     Vector3 defaultScale = new Vector3(1f, 1f, 1f);
     Vector3 fixedScale = new Vector3(-1f, 1f, 1f);
 
 
     void Start()
     {
         // Check for device cameras
         if (WebCamTexture.devices.Length == 0)
         {
             Debug.Log("No devices cameras found");
             return;
         }
 
         // Get the device's cameras and create WebCamTextures with them
         frontCameraDevice = WebCamTexture.devices.Last();
         backCameraDevice = WebCamTexture.devices.First();
 
         frontCameraTexture = new WebCamTexture(frontCameraDevice.name);
         backCameraTexture = new WebCamTexture(backCameraDevice.name);
 
         // Set camera filter modes for a smoother looking image
         frontCameraTexture.filterMode = FilterMode.Trilinear;
         backCameraTexture.filterMode = FilterMode.Trilinear;
 
         // Set the camera to use by default
         SetActiveCamera(frontCameraTexture);
     }
 
     // Set the device camera to use and start it
     public void SetActiveCamera(WebCamTexture cameraToUse)
     {
         if (activeCameraTexture != null)
         {
             activeCameraTexture.Stop();
         }
             
         activeCameraTexture = cameraToUse;
         activeCameraDevice = WebCamTexture.devices.FirstOrDefault(device => 
             device.name == cameraToUse.deviceName);
 
         image.texture = activeCameraTexture;
         image.material.mainTexture = activeCameraTexture;
 
         activeCameraTexture.Play();
     }
 
     // Switch between the device's front and back camera
     public void SwitchCamera()
     {
         SetActiveCamera(activeCameraTexture.Equals(frontCameraTexture) ? 
             backCameraTexture : frontCameraTexture);
     }
         
     // Make adjustments to image every frame to be safe, since Unity isn't 
     // guaranteed to report correct data as soon as device camera is started
     void Update()
     {
         // Skip making adjustment for incorrect camera data
         if (activeCameraTexture.width < 100)
         {
             Debug.Log("Still waiting another frame for correct info...");
             return;
         }
 
         // Rotate image to show correct orientation 
         rotationVector.z = -activeCameraTexture.videoRotationAngle;
         image.rectTransform.localEulerAngles = rotationVector;
 
         // Set AspectRatioFitter's ratio
         float videoRatio = 
             (float)activeCameraTexture.width / (float)activeCameraTexture.height;
         imageFitter.aspectRatio = videoRatio;
 
         // Unflip if vertically flipped
         image.uvRect = 
             activeCameraTexture.videoVerticallyMirrored ? fixedRect : defaultRect;
 
         // Mirror front-facing camera's image horizontally to look more natural
         imageParent.localScale = 
             activeCameraDevice.isFrontFacing ? fixedScale : defaultScale;
     }
 }

Comments on Fattie's Answer:

So I'm pretty sure at t$$anonymous$$s point that "verticallyMirrored" means that a rotation about the horizontal axis is needed. So I've modified the code in Fattie's answer to:

    int ccwNeeded = -wct.videoRotationAngle;
    
    rawImageRT.localEulerAngles = new Vector3(0f,0f,ccwNeeded);
    
    float videoRatio = (float)wct.width/(float)wct.height;
    
    rawImageARF.aspectRatio = videoRatio;
    
    if ( wct.videoVerticallyMirrored )
      rawImage.uvRect = new Rect(0,1,1,-1);  // flip on HORIZONTAL axis
    else
      rawImage.uvRect = new Rect(0,0,1,1); // no flip

i.e. I removed "if ( wct.videoVerticallyMirrored ) ccwNeeded += 180;" and changed the flipped uvRect values. I'll post a new answer here or somewhere on t$$anonymous$$s site with my full script once I iron it out w$$anonymous$$ch includes using both front and back cameras and mirroring the front camera's texture to make it more natural.

Have you tried NatCam? It works wonders and has a lot more features.

Unity 5.6.1 Release Notes [Extract]:

• Android: Fixed WebCamTexture crash with denied permissions. (877837)

• Android: Webcam - Fixed the wrong orientation returned on first frames. (875247)

Hope t$$anonymous$$s solves a small issue faced here.

Hey I was having good fun with t$$anonymous$$s on iOS, but I resolved it in the end with somet$$anonymous$$ng pretty short and sweet.

I still needed to wait for the WebCamTexture.width to be more than 100 before adding it to the raw image texture/material and then I used SetNativeSize() on the raw texture. Here is my code for initialization:

         private IEnumerator WaitForWebCamAndInitialize( WebCamTexture _webCamTexture ) 
         {
             w$$anonymous$$le( _webCamTexture.width < 100 )
                 yield return null;
 
             _isWebCamSet = true;
             _rawCamImage.texture = _webCamTexture;
             _rawCamImage.material.mainTexture = _webCamTexture;
             _rawCamImage.SetNativeSize();
 
             StartCoroutine( FadeToCameraView() );
         }

FadeToCameraView() does as it suggests.

I also had to rotate the rect transform negative 90 on the z axis because the app runs in portrait mode only and the raw data from the iOS camera seems to be aligned with landscape mode. Now everyt$$anonymous$$ng works like a charm on iOS, but testing on the iMac shows the image rotated by the negative 90 I gave it.

Hope that helps someone