This thread is resolved. Here is a description of the problem and solution.
Problem: The Chinese (simplified) flag is missing on my Frontend and Backend.
Solution: #1 As this is not causing any other issues you can download the flag here https://wpml.org/wp-content/plugins/sitepress-multilingual-cms/res/flags/zh.png and upload it under WPML -> Languages -> Edit Languages as "Custom Flag".
#2 Or upload it to wp-content/plugins/sitepress-multilingual-cms/res/flags/zh-hans.png
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