question

The problem is how the model is structured in Sketchup.

Sketchup allows you to assign textures on a per-face basis. FlexSim only allows you to assign textures on a per-mesh basis.

See also Textures on skp file not showing.

In Sketchup, the "dome 2014" component has the blue water material assigned as its primary material. Then several of the individual faces of that component have been painted on one side with different materials (the marble base and the wooden doors). The other side of those faces is also still the blue water material:

Also, Sketchup doesn't correctly export this shape as it is into any of the formats I tried (fbx, 3ds, dae). Sketchup doesn't give you much control over the actual shape data, and the way it structures its data doesn't align well with how 3D shape data is stored in other file formats and programs.

You can fix this shape in Sketchup by cutting the non-water faces out, pasting them as new components, and assigning one material to each component. See Sketchup Hint: Making parts of a skp file show the Flexsim color for more details on working with components in Sketchup.

Here is an updated version of the file with those faces cut out into their own components: 17679-untitled-pb1.skp