In case you haven’t noticed, your iPhone does not have a USB port. So you can’t connect a USB flash drive to it without an adapter. You don’t have to look for an adapter when you can use these wireless USB solutions to access USB flash drives on your iPhone or iPad:
HyperDrive iUSBport2: a wireless USB port hub for iOS and Android devices. It has 2 USB ports and accepts SD cards. It lets you perform 2-way file transfers between any USB drive & up to 12 different mobile devices at the same time.
HooToo TripMate Wireless N Portable Travel Router: turns any wired network into a wireless network instantly. It has a built-in 5200 mAh battery pack and is NAS enabled, so you can share data between your USB device and iPhone.
RAVPower FileHub Wireless SD Card Reader: a wireless SD card reader and USB storage solution for iOS devices. It has a 3000 mAh battery also. You can connect it to up to 5 devices at the same time.
Kingston Digital MobileLite Wireless Flash Reader: a compact Flash card reader that allows you to download your photos from your phone’s camera roll to a USB drive or SD card. You can stream movies to up to 3 users simultaneously via WiFi.
SanDisk Connect 32GB Wireless Flash Drive: lets you wirelessly store and share content across your smartphones, tablets, and computers. It can access data on up to 8 devices via WiFi.
SanDisk Connect 64 GB Wireless Media Drive: it has 64 GB built-in Flash storage and a SDHC/SDXC memory card slot. Optional WiFi password protection is available. The device is compatible with Kindle and Android gadgets too.
EasyAcc WiFi Wireless USB Flash Drive / SD Card Reader: a wireless USB hub for your iPhone. Lets you transfer photos/movies/music between mobile devices. It supports AirPlay. It can also serve as a portable WiFi repeater.
As you can see, you don’t need to use an adapter to connect USB flash drives to your iPhone. Not when you have one of the above wireless USB hubs.