Is this Yongnuo specific model able to be fired in slave mode by another flash?
Yes. The Yongnuo YN565EX III has S1 and S2 slave modes that allow another flash to send the "fire" command to the YN565EX III.
- In S1 mode the YN565EX III will fire when it detects a bright flash of light.
- In S2 mode the YN565EX III will ignore the first set of short bursts, such as a preflash emitted by the other flash being used in TTL mode, and (hopefully) fire when it detects the main flash.
The popup flash on your Rebel T6/1300D, like pretty much all popup flashes, is fairly weak and using it to trigger an off-camera flash will be difficult in certain situations which would include:
- Using the external flash enclosed inside flash modifiers
- Under certain types of flickering ambient lighting, such as older style fluorescent lighting
- An environment with pulsing lights such as a dance floor
In more controlled settings, the popup flash may be adequate. Although optical triggering typically requires line of sight between the master and slave flash, in a studio with subdued lighting it may be possible for enough of the light from the master flash to bounce off walls and trigger the slave.
Many relatively new Canon EOS bodies will also allow the popup flash to wirelessly control a YN565EX III to set things such as manual flash power and even use the YN565EX III in TTL mode. But the popup flash in the Rebel T6/1300 is not a Canon wireless optical system "Master" flash like the popup flash on cameras like the 70D and later x0D models or the Rebel T4i/650D and later Txi/xx0D models.
Any hot shoe flash mounted on your camera that is a Canon optical E-TTL "Master" flash will control your YN565EX III and allow you to control the YN656EX III from the control panel of the "Master" flash.
Any other manual flash with no pre-flashes (for E-TTL or red-eye reduction, etc.) will be able to "fire" the YN656EX III in S1 mode.