Thank you for joining the Intel® communities.
At this point I would recommend updating the BIOS to the latest version if you don’t have the latest version, you can download it here.
Please follow the steps to do a BIOS update.
You can also try with a SSD firmware update, you can contact you SSD manufacturer for support about an SSD firmware update or if you are using an Intel(R) SSD you can download the tool you need here.
Also, you can follow the steps to do an Installation from USB stick at:
I hope this information is useful for you.
I strongly suspect your problem lies with your USB thumb drive rather than the NUC.
Try reformatting and writing your thumb drive. YUMI works well for me:
I have installed 15.04 and 15.10 on a NUC5i5RYK in UEFI mode (legacy boot off in the bios, it will not harm a Windows 7 dual-boot which needs legacy as GRUB creates a UEFI wrapper around it.) Do not try 14.04 there is no graphics support in the kernel as it is too old for Broadwell.
The problem you experience is your USB stick. Download a proper ISO of a distro containing a kernel no lower than 3.19. If on a Linux computer use this command:
dd if=<file> of=<device> bs=4M; sync
device is the usb you plugged in.. usually /dev/sdb look at dmesg after you plug in to see which device it actually is.