If you have a mac compatible capture card, you can stream with just FMLE but you wont be able to use anything other than the capture card input.
However, you can take the capture card into CamTwist and organize it similar to OBS or XSplit with your webcam/microphone.
If you're using an emulator or playing a pc game, I think camtwist can capture screen regions but I'm not sure. If not, no idea where to go from there.
As a guy with a mac, I know how much it sucks to hear this, but if you're really into the idea of streaming, you should install win7 on bootcamp and just switch over when you want to stream. It is much easier.
Obviously you need a tricaster but failing that check out CamTwist Studio (free).
*CamTwist looks like it struggling to keep up with OS X innovation. It might not even work anymore. You'll just have to investigate and see. Otherwise, you can look at something like BoinxTV which is in the hundreds-of-dollars range.
It only records what is on the screen, you can't overlay. I guess you could put your camera in a small window and put it on the screen.
You could, however, use http://camtwiststudio.com/ to actually embed your video over your desktop/camera feed.. I dunno, I'd have to play with it.
So yea, Quicktime is very basic, and would require custom hacks to do anything really outside of screencasting.
I've tried CamTwist + CocoaSplit, and it seemed to work, though audio was a bit glitchy (I used SoundFlower to get commentary audio mixed in, however the problems may have stemmed from the audio driver weirdness of using a hackintosh setup). I have very little knowledge on what the best settings are to get it all running smoothly, but it seems like a good jumping off point to work from.
CamTwist - http://camtwiststudio.com
CocoaSplit - http://krylon.rsdio.com/zakk/cocoasplit/
SoundFlower - http://cycling74.com/soundflower-landing-page/
Apparently the 5D3 isn't supported by Canon's new USB-to-webcam utility, I had been using v002-Camera-Live plus CamTwist Studio.
It definitely does not sustain 60 FPS (I see duplicated and torn frames in the output, probably closer to 30 FPS in reality), and the max resolution that CamTwist offers is 720p. Image quality looks great though and I bet this would be fine for streaming.
The 5D3 is only USB 2, so the max datarate from my camera can't exceed 480Mbit/s in any case.
Camtwist already does this for free. I can run a camera into my Mac and Camtwist tells the system it's a webcam. It also sends any program window or full-screen as a webcam (rather than as a screen-share).
Or Syphon, which is a protocol that lets various systems graphics processes talk to one another between programs. I use it for VJ / theatrical visuals, i.e. sending a Qlab or Isadora feed into Zoom, or sending an iPhone camera wirelessly to a projector via my VJ software.
There's some updates that kill these kind of powers but they often come back again as software fixes happen.
Everyone else is saying it's impossible because copyright and ownership, but I guess it must be a Mac thing, because I'm not at all having this problem on PC. Amazon, Hulu, Netflix, Xfinity... I've streamed anything and everything without problem.
Mind you, I'm almost always sharing the whole screen, and not the lone application. No idea if that makes a difference.
I do occasionally have to stream certain things using a screen capture virtual camera (and then on the application, stream my "webcam" which is actually the virtual camera). On Windows, I'd use OBS + VirtualCam. From a quick search it looks like you can do that on Mac using CamTwist.
Sorry that I can't be more helpful. I just want you to know that it's not 100% impossible to stream those sites.
There's an app called CamTwist that can add a bunch of effects to your webcam video, and one of them is to flip it left-to-right. I've used it in the past to fix exactly this issue, but I haven't had a chance to try it on my High Sierra systems yet. This app doesn't appear to quite be abandoned yet, but it hasn't seen a real recent update, either, so it's hard to say. Even so, it might be worth a try.
------------------
UPDATE: I just now tried a Skype call between a pair of iMacs both running the latest macOS (High Sierra 10.13.5) and the latest version of Skype and both the videos appeared as normal and were not mirrored. Both Macs were using the built-in FaceTime camera, but I've also done Skype calls with relatives using an external Logitech C920 webcam on an old 17" Macbook Pro and it's also not mirrored. This makes me wonder if this is a software version issue, since the only reason I have CamTwist was to deal with this issue, but it's been a few (several?) years since I had to use it.
Hey mate, sadly it's a windows machine, however I should imagine there's similar software for windows and I can look for it. I'm not having much luck yet, but I think that's because it's difficult to know what I'm looking for exactly. There's lots of livestreaming software, and all would use a webcam, and probably any camera hooked up to a capture card.
Making it work with (and convert) the output of the I/O card that feeds the client monitor is the interesting part that I'm struggling with. What is your setup exactly when you do this?
Are you using a blackmagic I/O card like ultrastudio for example? When you run camtwist, does it allow the I/O card to be a selectable device from which it captures and processes video? Does skype then use 'CamTwist' as a webcam?
I see on this section of the camtwist website that it works with capture cards http://camtwiststudio.com/works-with-hdmi-capture-cards/ But I only have playback card, and in any case, unless you can loop the ouput of a card that is both capture and playback, back in to itself, I'm curious how it works.
Camtwist may be your best option for recording the show. You can setup multiple cameras and have a simple on screen switcher to manipulate them http://robertbuzink.com/2012/livestreaming-with-multiple-usb-webcams/.
And then camtwist can be integrated into google hangouts http://www.success.grownupgeek.com/index.php/2013/03/16/how-to-use-camtwist-in-google-hangouts/
Best of all camtwist is free http://camtwiststudio.com/
Ive only recorded to Hangouts once, and with each host living in a different part of the world, we just recorded it to youtube, and then used a youtube ripping site (normally not legal, but since you created the content who cares). Converted it to an MP3 and then brought it in to audition.
This may be your most low cost option.
There is CamTwist but it's a cpu hog.
Alternatively there is the Multiplatform OBS beta which works fairly well as well, although it is still not quite there yet as a finished product.
Download CamTwist as well as Adobe Flash Media Live Encoder, then watch this video to learn how to get them set up to stream.