Unfortunately, Amazon left a basic headphone jack off of the Echo; I might add that many quality table radios have this handy and inexpensive feature. In that way you could have piped the audio into the stereo. Like you, I also can access DLNA devices on apps and connected to my stereo to play music, video, etc. The last thing I would want to send to the stereo is the Echo's output. What is nice is the Echo can play TuneIn stations without needing a gadget like a Roku and TV; the Echo is a self-contained system.
I find my Echo to be a nice and handy state of the art internet clock radio and weather/news reporter. I feel that out of the box, it came with bare minimum apps/channels very unlike, say, a Roku. Since one of my most-used internet radio apps (other than TuneIn) is Slacker (app like Pandora), but I cannot call up Slacker like I can Pandora, so I have to resort to BT-beaming Slacker from mobile device to Echo. The Echo needs a lot more channels than it has. I hope they will be coming along soon.