Fire TV is Android with an Amazon wrapper.
You can load apps on to it that support DLNA.
Just like you can load apps onto a plain vanilla Android box to support DLNA.
Kodi is a good example of a media player app that supports DLNA (and SMB) and will run on Android and Fire.
To the OP: if you’re stuck on a ‘Smart TV’, look for one that says it has a DLNA-compliant media browser/player, or can load apps to support it.
Like Shabuboy, I’m still not convinced that ‘Smart TVs’ are a good idea, although they are improving. Their app support is often very limited, often via their own, very limited app store; the apps available are not updated very often, and support for the device stops as soon as a new model is released, and there’s often a significant markup for ‘smart’ functions (although this seems to be falling rapidly).
There are hundreds of generic Android media boxes, supporting 4K, H265, etc. which will run a whole host of media apps straight from the Play store.
See this thread for a related discussion: