I obtained iron-free manganese dioxide (probably mixed with carbon) from a tantalum capacitor. It is quite uniformly black, with some silver electrodes connecting it to the current. When placed in cold hydrochloric acid, it releases a small quantity of chlorine gas and produces a brown solution. I initially thought that this was an indication of iron, but the solution decolorized when heated, showing that the manganese dioxide was relatively pure. It seems that manganese(III) is relatively stable as a chloro complex in cold solutions, but decomposes to chlorine and manganese(II) in hot solutions.
If you have a hard time bringing a hot plate or any other heat source outside to perform the reaction, you may absorb the chlorine produced by a tissue soaked in either ascorbic acid or sodium metabisulfite mixed with sodium carbonate. No chlorine smell will be produced until the tissue is exhausted of its chemicals. After the dissolution, pure manganese(II) chloride solution will remain. If you desire to keep a source of manganese ions, precipitate the manganese as the carbonate, which is resistant to further aerial oxidation, unlike the hydroxide. Manganese(II) chloride can be evaporated but it needs to be stored in a tightly sealed container to avoid any deliquescence.
Manganese dioxide from an alkaline battery or a carbon-zinc battery is more problematic. In these, large quantities of iron impurities are generally present, which can be difficult to extract. Occasionally, you may find a battery that happens to be free of iron impurities. If so, a colorless solution will be formed upon heating the manganese dioxide with hydrochloric acid. Otherwise, a dirt brown solution will form. This may be remedied by dissolving the manganese dioxide in sodium metabisulfite solution. The sulfite will reduce the manganese(IV) to soluble manganese(II), while the iron(III) remains untouched.
You may get purer manganese dioxide from 3 volt lithium coin cells. I generally have had better experience with these than with alkaline batteries, but they are much more expensive than the aforementioned batteries. Once I got a batch of pure manganese(II) chloride from an unknown alkaline battery.
Extracting pure manganese salts from batteries is difficult, but the fact that manganese(IV) is a stronger oxidizer than iron(III) is useful to know.