Can aluminum and hydrochloric acid be used to generate hydrogen gas? I am looking to produce hydrogen gas in a small amount with supplies I currently have. Most of the methods I have seen involve reacting zinc or magnesium with $\ce{HCl}$ to obtain the gas, but I do not have zinc or magnesium at the moment.

Is there any reason why aluminum cannot be used just as effectively as zinc? According to the reactivity series, aluminum should be even more reactive than zinc.
Yes. See this video for a demonstration. 

The reaction is:
$$\ce{ 2Al (s) + 6 HCl (aq) -&gt; 2AlCl3 (s) + 3H2(g)}$$

You can capture the hydrogen and proceed with your experiments.