You can scroll the Kindle's Wi-Fi Networks list, page by page, six networks per page. There are 9 networks showing on the Kindle as I write, six of them are VMxxxxxxx (so Virgin Media) in nearby locations. There are also a couple of BT hubs. But, alas, no sign of my hub. I have seriously to consider the possibility that Kindles cannot connect to Hub 4s. I'd love to be proved wrong.
I know this thread is a little old, but thought I'd throw in my findings having had the same issue with my PaperWhite 7th generation Kindle - and think I found the solution.
A while back I'd been connecting my PaperWhite to my HUB 4 without problems. I recently attempted to connect to the WiFi but no evidence of my router on the Kindle WiFi networks. "Somewhere" on here, someone mentioned setting the 2.4 GHz channel to between 1 & 11 (NO HIGHER !!). Bingo .... I remembered I'd set mine to channel 14 due to our neighbours darn Sky multi WiFi transmissions all over the place.
I set the 2.4 GHz channel to 11 (the quietest channel available when I used WiFi Analyzer app to check). Voiala - PaperWhite suddenly saw & connected to WiFi. As a test, I changed the channel to 12, 13, and 14 ... all failed to be seen.
So, login to your router on 192.168.0.1
Go to Advanced settings / Wireless signal / Set Channel to "MANUAL" / choose a channel between 1 and 11 / Apply changes.
Wait a minute or so for settings to save then refresh WiFi on your Kindle, and hopefully you'll see your Routers SSID.
Hope this might help and fix anyone else with the issue. Thanks to "whoever" mentioned channel 11 being maximum number to select. I can't immediately find the page again 👍
Re: Kindle not seeing / listing Hub 4 SSID (solved?)
Thanks for the advice.
I tried manually setting the channel to several single-digit settings. Nothing worked. My phone, computer, etc. all worked with any of the settings; only Kindles seem picky and will not show the correct Wi-Fi ID. They will show other IDs in the neighbourhood, just not mine. This is extraordinary as your supplied settings for a similar hardware do seem to work for you. Alas, I have several Kindles of varying vintages and they all refuse to cooperate. Hub 3 and previous were fine. All other devices are fine. Just my Hub4 and all my Kindles