"I want to run firestick with my projector which is ceiling mounted through my Samsung DVD player which only has HDMI out. My audio and video flows through the dvd player. When connecting directly to the projector I get video but no sound."
Your Samsung DVD would need an HDMI input in order for you to accomplish what you are trying. From your attached photo, it does not appear that the Samsung has such an input, which is not surprising, as most such devices do not have audio or video inputs -- only outputs.
What do you currently connect the audio output of your Samsung player to?