When using Flamingo nXt as the target renderer, there's a few things you may want to keep in mind.
Flamingo nxt doesn't support all features in Bongo. For example material change, Video Textures doesn't work, because it requires RDK support (the renderer features in Rhino). Flamingo nXt doesn't support the RDK.
However Flamingo nxt 5 does support the RDK, so if you want to animate those features, please get Flamingo 5.
Before you start the rendering, please make sure you've set the constraints on the rendering, either by restricting the time or the passes. Otherwise your rendering will never stop and move on to the next one.
If you're still not able to get the rendering to run or it stops after the first frame you need to enable the setting "Allow modeling while rendering". In Tools->Options->Rhino Options->Flamingo nXt.
Bongo 2 can animate the material properties in Rhino 5, so if the renderer supports this feature (the RDK in Rhino 5), Bongo will be able to animate the material properties. Unfortunately at the moment the Flamingo nXt library doesn't support it.
But Flamingo nXt supports Rhino Basic Materials, so if you make a Basic Material in Rhino 5 and animate it, Flamingo nXt should be able to render the animated material.
You start off by rendering and the texture looks correct.
In this case the best option is cube. After changing the mapping -setting, the texture follows the object.
You've set the Output resolution in Bongo to be HD (1920x1080), but the rendered image is another size. What to do?
In order for Bongo to be able to affect the resolution in the Flamingo image, you have to set the Flamingo render resolution setting to "Image Size". Then Bongo will be able to change the render resolution in Flamingo.