Is there an OTG cable for the iPhone? Transferring files?

Yes you can with the correct hardware.

Here are some of the options.

Here is an external wifi hub that lets you attach flash drives.

Allows you to access your own sd card and usb devices

http://www.amazon.com/Dane-Elec-Media-Streamer-Mobile-Junkie/dp/B00IA8LLUW

suggested by seeblue

http://www.dpreview.com/forums/thread/3516024

Airstash
"Easily access, transfer, and stream your files from AirStash® – the pocketable wireless flash drive for iPad, iPhone, and iPod touch! This app requires an AirStash device in order to work. View, import & export photos, wirelessly stream videos, music & podcasts, and view documents stored on your AirStash. AirStash+ is an enhanced alternative to the built-in web interface adding features only possible with a native app."
http://www.airstash.com/

SanDisk
" SanDisk Connect Wireless Stick is the flash drive reinvented to work with both your computer and your mobile devices."https://www.sandisk.com/home/mobile-device-storage/connect-wireless-stick

Seagate Wireless portable hard drive
"The new 500GB Seagate Wireless portable hard drive is the company's latest HD designed specifically for use with tablets and smartphones like Apple's iPad and iPhone."
http://www.macrumors.com/2015/01/04/seagate-ces-2015-new-products/

Camouflage data files as a raw image.
read files from a flash drivehttps://www.youtube.com/watch?v=m5f1VmjjczQ

Kingston Digital MobileLite Wireless Flash Reader for Smartphones and Tablets (MLW221)
Kingston Digital MobileLite Wireless Flash Reader for Smartphones and Tablets (MLW221)


FlashAir™ II Wireless SD Card series

--Share photos & videos wirelessly

--Capacity 16GB

--Supports simultaneous access from up to seven devices

http://us.toshiba.com/accessories/wireless-sd/16gb/class-10/PFW016U-1CCW

Photofast's iFlash Drive
Here is a nice adapter. You can move data in both directions! Be sure to get the real thing.
http://www.photofast.com

review:
http://www.macworld.com/article/2036911/review-i-flashdrive-hd-a-flash-drive-for -ipads-iphones-and-laptops.html

Here is the ios app:
https://itunes.apple.com/us/app/i-flashdrive-hd/id525386291?mt=8

The app get some bad reviews. Turns out there is a cheap imitation product that didn't develop their own software and parasites of of PhotoFast's software. Could be the folks using the imitation product are complaining.

Yes and No.

The Camera Adapter Lightning to USB cable is able to connect a USB device/stick/drive to the iPhone - however, it is only very recently that iPhone was able to make this connection with the adapter, as it is usually only compatible with the iPad.

At the moment I have not been able to successfully transfer files from my iPhone to a USB drive via the adapter cable - but I can connect to a USB microphone through the cable, which is a big step forward for Apple.

Perhaps for now, try looking into using the iStick or alternatively, downloading an App that can see to your iPhone uploading pics to cloud-based platforms that are not limiting like iCloud.

Hope this helps in some way - I realise it is quite a long time since you posted your request but any answer is better than none, right?

Sounds like you need this my friend! I use this every actually and its wireless! I use it to store my music so I don't have to sync with iTunes. Pictures transfer flawless also! You can connect threw USB on a pc and retrieve all information you stored from your I device.

https://www.sandisk.com/home/mobile-device-storage/connect-wireless-stick

No.