Doesn't really matter what brand you buy right now. They pretty much operate the same way.
There is one possibility but I doubt your audio settings on your TV will include a Bitstream/PCM output selection for your TV set.
TVs use PCM coding on HDMI inputs. Your amp prefers Bitstream.
This is usually adjustable on Blu Ray DVD players (with internet connectability) so you can set it on those. My BD-D6700 from Samsung delivers Netflix audio to my Audio Amp (Denon AVR-787). I set mine to bitstream.
The problem with your setup is that you are connecting Netflix directly into your TV set and hoping the Optical output OR HDMI with ARC can deliver it back to your Amp.
The problem could simply be you chose the wrong way to deliver it to your amp, OR neither will function by converting the data stream and delivering it's audio to the two possible outputs.
This is what I would do in YOUR SITUATION
Fire up Netflix...see if the TV speakers work.
If it does, then the TV can deliver sound to it's own speakers and you know the TV is processing audio.
Next -- whatever connection you are using....try the other.
(You never did give me your TV's Model number, nor your amp's model number, so I'm working in the Dark here. Give me some insight so I can read and give you better details)
If you have ARC on HDMI, connect Optical OUT from the TV to the amp and try that.
If anything, Optical will probably get audio to your amp from Netflix.
And if not....that's why they made it available on BLU RAYs before they did it on TV sets.
Everybody can afford a Blu Ray a whole lot easier than they can afford a TV set..
Makes sense the licensing is taken care of faster on those.
Like I said, I'm using it on my Brand New Samsung BD-D6700.
I bought it at Tiger Direct on Monday, got it yesterday (Free shipping, not overnighted) and just hooked it up this morning. Watching Bleach on Instant Downloads.
It may not be what you want to hear as your answer, but it is ONE WAY to get NETFLIX to your AMP.
So, do us both a Favor. Consider that option, but Puh--LEEZE get me your TV and amp's model numbers!
I can't be concise without it.
Generalities don't cut the mustard. I Prefer specifics.