As you mentioned, iPhones only support Airdrop. Airdrop limits a lot the iPhone's Bluetooth/Wi-Fi capabilities since it's only compatible with other iDevices. So, I believe this won't be possible on an iPhone or for this purpose any iOS device.
On the other hand if you want to use an Android device, it depends on how you want to transfer, do you want to transfer the pictures over Wi-Fi or Bluetooth?
Either way has one main option available that comes to my mind. If you choose Bluetooth, you could use the FTP profile, of which you can learn more of in section 6.13 of the Intel® Edison Bluetooth® User Guide. If decide to use Wi-Fi, I believe Wi-Fi Direct (P2P) would be your best approach, you can learn more about this on section 6 of Intel® Edison Wi-Fi User Guide.