What rtmp streaming software solutions exist?
Try influxis.com, it's web based but you could get your cam streaming pretty quickly. There are free options also like Red5, it's open source and it doesn't use FMS.
3 possible alternatives to using FMLE.
Vidblaster Home is another alternative to Wirecast & FMLE.
Also, you could go the route of using a hardware encoder like Hauppauge Stream-ez Pro.
Finally, if your current hosting solution using Wowza Streaming Engine as their server side software, you can utilize a basic IP Camera like the Axis M1025 Network Camera.
I setup nginx with the open source NGINX-based Media Streaming Server project recently and used Open Broadcaster Software to stream to it.
I was able to watch the stream using both Kodi and VLC.