Water has a low viscosity (thickness). How might the movement of the dyes

change if a fluid with a higher viscosity is used?

If a fluid with a higher viscosity is used, the movement of the dyes will likely be slower and more sluggish. The higher viscosity will result in greater resistance to flow, causing the dyes to move more slowly through the fluid. They may also spread less and have less diffusion.

By the way viscosity is not thickness. It is more like stickiness, resistance to shear.