Hello Lucas,
Yes, this is possible.
It looks like you're confusing RTSP and RTMP here. I'm not sure exactly how you'd use VLC to stream out over RTMP, but the following ffmpeg command should work for you:
raspivid -o - -t 9999999 -w 1280 -h 720 --hflip | ffmpeg -i - vcodec copy -f flv rtmp://localhost/live/STREAMNAME
Replace "STREAMNAME" with the name of the stream you configured, and it should work.
Additionally, in the "source" setting, do not specify a port. "push://127.0.0.1:1935" will not work, but "push://127.0.0.1" will. You can also use "push://localhost" - both values should work, but the latter also allows pushing over IPv6 instead of only IPv4. Or, if you don't care about security in this case, a simple "push://" will allow pushes from anywhere.
Hope that helped! Let me know if you run into any problems.
Regards,
Jaron Viëtor
CTO, DDVTech