Is .NET 3.5.1 Supported on Windows Server 2016?

Yes, Net Framework 3.5 is working on Windows Server 2016, I have it installed on my Servers. So far, we haven't had any reported issues from our programmers.

Remember, You need to install it as a server feature. (Make sure to Specify an alternate source path during the installation. You need to mount your Windows 2016 Disk and set the path to Drive:\sources\sxs).

Microsoft has updated their FAQ

https://support.microsoft.com/en-us/help/17455/lifecycle-faq-net-framework

.NET Framework 3.5 SP1: Beginning with .NET Framework 3.5 Service Pack 1 (SP1) the .NET Framework is defined as a component instead of an independent product. So, support for .NET Framework 3.5 SP1 is driven by the Lifecycle Policy of the Windows operating system (that is, when Windows is in the Mainstream Support phase or Extended Support phase, so are its components). When a product such as Windows reaches the end of support, so do its related components. .NET Framework 3.5 SP1 is supported on Windows Vista SP2, Windows 7 SP1, Windows Server 2008 SP2, Windows Server 2008 R2 SP1, Windows 8.1 Update, Windows Server 2012, Windows Server 2012 R2, Windows 10, and Windows Server 2016 according to the end of support date for each operating system.