Well, here's another reason to not love this new site.
I don't have the resources that Facebook et al have to test every browser and device to ensure a smooth launch. Glitches are inevitable especially when it's newer technology and more obscure browsers.
The post processing is done on a backend machine via a queue so may not happen immediately (it's 'async' to those in the know). Because of this, the client needs to be notified when the post has actually been processed and it opens a push channel to do this - it's possible that the Kindle doesn't support this but also possible that there's a bug - I did fix something this morning related to the channel token expiring.
If the post has been submitted and it's queued then you don't have to wait - it will appear once it's been processed - I will look at adding better error handling and a timeout so it can stop waiting if it get's stuck or at least let you know differently (if the browser doesn't support it)
We'll work through the issues and I'll try to address as many of the compatibility issues as I can.