Altium error: Nets containing multiple input ports. What does this error mean?
With "Flat (Only ports global)" scope selected, "...net labels are local to each sheet; they will not connect across sheets. All ports with the same name will be connected, on all sheets."  - Altium "Multi-Sheet Design" 

This seems like it should be OK for what you are trying to do, but I think in this type of design setting, there must be a 1:1 relationship of Input and Output port. In the flat design case, the input ports are connected to each other, hence the "multiple input ports" error. Here are a couple things you could try:


Switch to a Hierarchical design
This requires you to use a Top sheet to control the design hierarchy. Review "5.1.3  Constructing the top sheet" in the previously mentioned training module. For what it's worth, all of my designs are of this design setting.
Change Input ports to Bidirectional

This may make the error go away (due to your project's Connection Matrix), but it might not make sense from a real-world viewpoint. The CLK/SDI lines are most certainly not bidirectional. This might cause problems when you are in a design review and have to explain why you've marked everything as bidirectional.
Edit the connection matrix
Stick with your flat design setting, but tell Altium to shove it by editing the Error/Warning connection matrix:


Now multiple input ports will only be reported as a warning, not a show-stopping error.