Can the titrant and the unknown material be flipped?
The titration reaction does not know or care whether one reagent is in the buret and one is in the conical flask (Erlenmeyer flask, it is not a beaker in your figure). And certainly you can standardize/titrate potassium permanganate with ferrous ammonium sulfate solution to determine the concentration of permanganate ion. Ferrous ammonium sulfate hexahydrate is a primary standard in analytical chemistry.

If you are extraordinary careful, you can fill the iron (II) solution in the buret and have permanganate in the conical flask. The end-point will be slightly vague (deep purple to colorless). You really have to be extra-cautious. The question is why bother with this painful eye-stressing procedure? Always take the permanganate in the buret.

A dark solution can be used in the conical flask. For example, in iodometric titrations, we start with a deep brown solution, which fades, to nearly a colorless solution upon titration with thiosulfate. In order to confirm the end-point, you would put a drop of starch before your expected equivalence point. Again, the color change is from deep blue to colorless.