Determine if stuff is Potassium Alum
From Wikipedia:

An alum is a type of chemical compound, usually a hydrated double sulfate salt of aluminum with the general formula $\ce{XAl(SO4)2 · 12 H2O},$ where $\ce{X}$ is a monovalent cation such as potassium or ammonium.

There are also chromium alums and ferric alums, but the color in your sample does not seem to suggest either of them.
The alums melt at relatively low temperatures, because they already have a lot of water in the crystal structure, so ammonium alum and potassium alum can not be differentiated on the basis of melting points. Solubilities are fairly close, too:
$$
\begin{array}{llc}
\hline
\text{Compound} &amp; \text{mp}/\pu{°C} &amp; \text{Solubility}/\% \\
\hline
\ce{(NH4)Al(SO4)2 · 12 H2O} &amp; 93 &amp; 15 \\
\ce{KAl(SO4)2 · 12 H2O} &amp; 92.5 &amp; 11 \\
\hline
\end{array}
$$
If there is no violet color to a flame, there may be no potassium, but the test can be sensitive and may be indeterminate. Eliminate the possibility that the alum is an ammonium salt by dissolving some in water and adding a strong alkali, then sniffing it gently. If you smell ammonia, you have an ammonia alum; it will still work as a flocculant for muddy water, but is different chemically. A strong alkali readily available at home, well, at the grocery store anyway, is sodium carbonate (washing soda).