AirPlay/DLNA Receiver (PRO) has proven to be VERY reliable and functional on my FireTV. I use it all the time, for flinging content (audio and video) from my laptop and smartphone. Fullscreen mirroring works, too.
Sure, it works a bit better on my AppleTV 3, but my point is, the statement that "the biggest downside with Fire TV is that there are zero apps that are even close to reliable and fully functional with AirPlay" is demonstrably incorrect.
Doesn't the macbook have it's own casting option like the iphone does? if so you should get this.
https://www.amazon.com/x5434-x6C5D-AirPlay-DLNA-Receiver/dp/B00LAT7QV6
It always works for me using my iphone and it's on sale for $2 instead of the normal $5.
It's not free, but it's not ridiculously expensive… http://www.amazon.com/x5434-x6C5D-AirPlay-DLNA-Receiver/dp/B00LAT7QV6
I know it works. And it works well. It's only a mirror option though, so you can't use your device while watching a different app. I'm on an SE 9.3.2, bit I've mirrored an iPad Air on 8.0.4, and an iphone 6plus on 9.0.2, and an iPod touch on 9.0.2 They all work the same way and they all work well You can also try before you buy if you just download the apk and side load it. It will eventually do a license check though and stop working. Just buy it through your fire tv interface $5
I've been using my FireTV and the same single app for almost two years now with literally zero issues. It's 100% reliable.
I can't account for whatever apps you tried, but the one I have works perfectly fine. http://www.amazon.com/x5434-x6C5D-AirPlay-DLNA-Receiver/dp/B00LAT7QV6
Had to try a few apps for this but ultimately landed on http://www.amazon.com/gp/product/B00LAT7QV6
Paid the $4.99 but you get a solid, always-on, AppleTV-like mirroring and AirPlay setup.
Edit: Woops, re-read what you're asking and my suggestion is for the reverse of this. Not sure why you'd want your FireTV on your phone when every app is available. If you want to send your phone to the FireTV, then the above works great.
AirPlay works on my FireTV thanks to this app. Loaded normally, no sideloading required, and ... it works fine.
I am using AirplayReceiver Pro since months and never an issue.
I can stream videos (from apps and safari), audio and mirror.
I am honestly impressed how smooth it is, maybe I am just lucky but I use it daily and never a small issue.
It doesn't work with the official youtube app but I found an app called protube which works better and remove the ads.
No sure about CTV GO app.
The main reason: it has a menu system and a remote; no phone, tablet, or computer needed. Real access to Amazon Instant. Also gets you access to lots of compatible Android apps in the Amazon store; one of the more useful apps to me is one that enables AirPlay for my Apple devices.
Also, better hardware: dual-band wifi (instead of single), dual core cpu (instead of single), twice the ram, four times the local storage. Also supports Miracast.
Best Buy and Staples are selling them in-store for $25.
I use this: https://www.amazon.com/gp/product/B00LAT7QV6
Google Play link is here: https://play.google.com/store/apps/details?id=com.waxrain.airplaydmr3
I use it on my Android 10 TV box and it works pretty well. I hadn't had any issues with photos or playing videos - I have seen some stuttering unlike my Apple TV box but for $5, I thought it was totally worth it.
I usually get these apps via Amazon App store since it lets me download it to my Amazon Firesticks easier - and on other Android devices, I just have to install the Amazon App Store.
Haven't used it. Not recommending :)
Aw shucks is correct. The app u/instantbitsapps made called web video cast is excellent. I'd love to see it on iOS. Very active Dev updates the app frequently.
iOS options:
Rocket Fire Video Cast for Amazon TV: Best browser to streams movies using Fling by Omar Mody https://appsto.re/us/1Rcuz.i
iWebTV for Chromecast, Fire TV & More - cast, stream & watch online videos with the best by Swishly inc https://appsto.re/us/XtPK7.i
Video & TV Cast for Fire TV: Best Browser to stream any web-video on HD-TV displays by 2kit consulting https://appsto.re/us/flWy6.i
Or AirPlay to this app (it will not do DRM protected content): http://www.amazon.com/x5434-x6C5D-AirPlay-DLNA-Receiver/dp/B00LAT7QV6
This one is what I use http://www.amazon.com/x5434-x6C5D-AirPlay-DLNA-Receiver/dp/B00LAT7QV6
Should be this one - http://www.amazon.com/x5434-x6C5D-AirPlay-DLNA-Receiver/dp/B00LAT7QV6
I use this one - http://www.amazon.com/x5434-x6C5D-AirPlay-DLNA-Receiver/dp/B00LAT7QV6
There are others that work though.
Don't mind at all. Here's a link.
There's an app called Airplay DLNA Receiver that I use on my Fire TV. It's been great so far. Has AirPlay and mirroring.
This is the best solution. http://www.amazon.com/x5434-x6C5D-AirPlay-DLNA-Receiver/dp/B00LAT7QV6 But I run into den issues with some apps like YouTube
I've used this app with very good success, sending AirPlay video from my Mac or iOS devices, to my FireTV:
https://www.amazon.com/x5434-x6C5D-AirPlay-DLNA-Receiver/dp/B00LAT7QV6