How to Hide an Application from Windows Taskbar

It's something of a hack job, but this might do the trick! It requires doing a bit of registry editing to shrink the taskbar icons so that the labels auto-hide.

Set taskbar options

1. Open Taskbar properties.
2. In the "Taskbar Appearance" group, change the "Taskbar Button" option to "Never combine" if you don't want stacking.

Adding/editing the registry entry

1. Press Windows Key + R to open the run command
2. Type int "regedit" (without quotes) and press OK
3. Go to HKEY_CURRENT_USER -> Control Panel -> Desktop -> WindowMetrics
4. Find the "MinWidth" entry.
5. If it is not there, right click on an empty space and select New -> String Value. Name this entry "MinWidth" (without quotes)
6. Double click on the MinWidth entry. If you want just the buttons to show, set this to 38 if you're using small buttons, 52 if you're using large buttons (or 54 in Windows 8). Otherwise any value above 38 will work. If you set a value below 38, the buttons will behave oddly. If your main display (on Windows 8.1 or later) has non-standard DPI (e.g. it's Retina or 4k display) you might need to multiply these numbers by the factor of 1.25, 1.5 or 2. Otherwise buttons will shrink / animate incorrectly.
7. Log off and log back in or restart to see the changes.

Deleting/Uninstalling

1. Press Windows Key + R to open the run command
2. Type int "regedit" (without quotes) and press OK
3. Go to HKEY_CURRENT_USER -> Control Panel -> Desktop -> WindowMetrics
4. Find the "MinWidth" entry and delete it.
5. Log off and log back in or restart to see the changes.

Steps to disable flashing icon on Taskbar - Windows 7

1. Click the Start icon
2. Type in regedit
3. Select regedit from the top of the result
4. Go to: HKEY_CURRENT_USER\Control Panel\Desktop
5. Editing ForegroundFlashCount
   1. Find ForegroundFlashCount
   2. Double click ForegroundFlashCount
   3. Replace the value for Value Data with 1
6. Editing ForegroundLockTimeout
   1. Find ForegroundLockTimeout
   2. Double click ForegroundLockTimeout
   3. Replace the value for Value Data with 0
7. Reboot

This is the way to do it without any 3rd-party applications. The steps are in detail steps to help both experienced and non-experienced users. If you want to undo these changes, repeat the steps above using the original values: ForegroundFlashCount is 7; ForegroundLockTimeout is 30d40.

Disclaimer : You should always backup your registry before editing your registry.