Install adb and fastboot for Oneplus 3

First install adb and fastboot:

sudo apt install android-tools-adb android-tools-fastboot

Now, add permissions for access as non-root user:
First we need to identify the tag of the device:
For any phone in fastboot, check without connecting device:

lsusb
Bus 002 Device 004: ID 0480:0210 Toshiba America Inc 
Bus 002 Device 003: ID 1058:0820 Western Digital Technologies, Inc. My Passport Ultra (WDBMWV, WDBZFP)
Bus 002 Device 002: ID 2109:0812 VIA Labs, Inc. VL812 Hub
Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 001 Device 008: ID 04f2:b56c Chicony Electronics Co., Ltd 
Bus 001 Device 007: ID 0bda:b008 Realtek Semiconductor Corp. 
Bus 001 Device 005: ID 046d:c534 Logitech, Inc. Unifying Receiver
Bus 001 Device 003: ID 1c4f:0002 SiGma Micro Keyboard TRACER Gamma Ivory
Bus 001 Device 004: ID 1d57:ad05 Xenta 
Bus 001 Device 002: ID 2109:2812 VIA Labs, Inc. VL812 Hub
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub

Now connect usb and retry:

lsusb
Bus 002 Device 004: ID 0480:0210 Toshiba America Inc 
Bus 002 Device 003: ID 1058:0820 Western Digital Technologies, Inc. My Passport Ultra (WDBMWV, WDBZFP)
Bus 002 Device 002: ID 2109:0812 VIA Labs, Inc. VL812 Hub
Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 001 Device 008: ID 04f2:b56c Chicony Electronics Co., Ltd 
Bus 001 Device 007: ID 0bda:b008 Realtek Semiconductor Corp. 
Bus 001 Device 005: ID 046d:c534 Logitech, Inc. Unifying Receiver
Bus 001 Device 003: ID 1c4f:0002 SiGma Micro Keyboard TRACER Gamma Ivory
Bus 001 Device 006: ID 18d1:d00d Google Inc. 
Bus 001 Device 004: ID 1d57:ad05 Xenta 
Bus 001 Device 002: ID 2109:2812 VIA Labs, Inc. VL812 Hub
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub

The additional line for the device is: 18d1:d00d Google Inc.

So create or edit the file /etc/udev/rules.d/99-android.rules as root:

sudo gedit /etc/udev/rules.d/99-android.rules

I added the following since I found the first one was for adb and the second in fastboot mode:

SUBSYSTEM=="usb", ATTRS{idVendor}=="2a70:9011", SYMLINK+="android_adb", MODE="0666" GROUP="plugdev"
TEST=="/var/run/ConsoleKit/database", 
RUN+="udev-acl --action=$env{action} --device=$env{DEVNAME}"

SUBSYSTEM=="usb", ATTRS{idVendor}=="18d1:d00d", SYMLINK+="android_adb", MODE="0666" GROUP="plugdev"
TEST=="/var/run/ConsoleKit/database", 
RUN+="udev-acl --action=$env{action} --device=$env{DEVNAME}"

Restart udev:

sudo service udev restart

You may need to restart linux.