Just download the Update.zip onto your device and flash it via TWRP.
Fastboot is not required this way.
The latest monthly release:
Update.ZIP_Nexus_Ryu_MXC89F-system-vendor.zip
This update.zip contains system.img and vendor.img only.
The May 2016 Google Nexus update for Pixcel C has included a new "bootloader" as well.
The Update.ZIP will not update the bootloader, pls use fastboot to update the bootloader.
If you want to install antoher kernel, pls use the following packages below:
Latest stock kernel:
Update.ZIP_Nexus_Ryu_MXC89F-kernel_dragon.zip
Latest xceed kernel:
Update.ZIP_Nexus_Ryu_MXC14G-kernel_xceed.zip
Latest phhusson kernel:
Update.ZIP_Nexus_Ryu_MXC89F-kernel_su-nocrypt-r205.zip
Prerequisites: installed TWRP custom recovery
xceed version: http://forum.xda-developers.com/pixe…ragon-t3288243
NYCHitman1 version: http://forum.xda-developers.com/show…&postcount=101
Root access:
If you have rooted your device you will not loose your root access by installing system.img and vendor.img.
SuperSU will be installed "systemless" on Pixel C, all the SuperSU binaries are still there -> on /data partition.
If you install antoher kernel you may need to re-root your device.
The guide for installing TWRP and Rooting is located here:
http://forum.xda-developers.com/pixe…ustom-t3307183
Download: https://onedrive.live.com/?authkey=%…9EB75F5DD9DA59
I will try to upload the Update.ZIP packages every month, as soon as possible. 
Have Fun !