Slack icon not visible any more in notification area
In Windows 10, you have to right-click on the tray (the area you referred to as "notification area") to be able to customize which icons are visible, choose Properties, and then click the Customize button.
From here, click “Select which icons appear on the taskbar”. Enabled items will show permanently on the tray bar.
Here you have a step-by-step guide to solve this issue.
Keep in mind, however, that the you also have to enable the option to "leave the application running in the notification bar" from Slack, as pointed out by Somnath Muluk
Additionally, every time there is a Slack client app update, you have to go into the "Select which icons appear on the taskbar" in Windows 10 to turn on the "new" icon. It seems this changes when the application is updated.
Update on August 5th, 2018. This issue has been around for nearly two years. I sent them this message on the 'help' issue I first submitted 19 months ago:
People,
This issue has persisted for over a year, and a Slack update this morning did the same thing - the icon is in the notification overflow window, instead of on the taskbar. If there is one application that MUST always be visible in the taskbar, it is Slack, and you keep falling down on this basic requirement.
Clearly, with every Slack client update, the operating system thinks it's a new app (with a new GUID or whatever the nomenclature is), so defaults to the notification icon being in the overflow. This is on you. No other application that uses notification icons does this after an update. None. Okay, maybe not none, but I have never encountered another one, and I am a super geek.
It also doesn't help, that after a client update, the old client runs until exited (as the taskbar icon remains visible), but on the next launch, the icon goes into the overflow. So it might appear to the uninformed that the Slack client update didn't trigger the problem, but it did.
Seriously, you need to mark this as important. It only takes about 10 seconds for us users to change the setting on the new icon, after we discover it's missing. But that 10 seconds is multiplied by the number of users who want that icon to stay visible, for every update. That is a LOT of wasted time.