You can produce metallic manganese using aluminium via the Goldschmidt process, more commonly known as the thermite reaction.
Experimental details here:
http://infohost.nmt.edu/~jaltig/Goldschmidt.pdf
The mangano-manganic oxide can be prepared by from the carbonate by heating.
The carbonate can be prepared from the chloride by precipitation with sodium carbonate.
Since manganese decomposes water even in the cold, I don't think that you will have success with a simple displacement reaction in aqueous solution.