You can't select multiple layers in the layers panel in GIMP. It's not possible. In any case, that's not how the Alignment Tool works anyway (*see note below).
You need to use the Alignment Tool Q to select the objects on the canvas for the alignment options to work. You can use Shift to select multiple objects, or you can click and drag with the tool to encompass the objects you want to select.
Each object needs to be on its own layer, and each of the layers must be cropped to their content (you can use Layer > Crop to Content)
Here's an example showing the tool working. You can see when each object is selected it gets four little square handles.
*Note: To be honest, the user manual doesn't really describe it well - it's quite poorly worded. Instead maybe check out this rather nice video tutorial on youtube which goes into some depth on how to use the tool.