The free clinic in my area, similarly staffed by medical students, is also staffed by pharmacy students and volunteer physicians and pharmacists.

There is a small pharmacy on site that is able to give out medications for free that have been donated by local hospitals, and pharmacy students and volunteer pharmacists keep track of the stocks, keep the formulary for the facility updated, recommend alternatives when the preferred medication isn't available, can act as consults for students or doctors when recommendations on poly-pharmacy, interactions, or equivalent dosage are needed, and of course package and dispense medications as well.

It sounds like your free clinic doesn't have an on-site pharmacy, and while that's something tough to start from scratch, you could at the very least start by talking to the clinic leadership, ferreting out free samples from drug companies or reps, and contacting local medical facilities for supply donations. Even the move from no on-site drugs to a free-sample closet could mean a big difference for people who need help month-by-month.

More suggestions: just make your skills known to the students and physicians so they know they can come to you for recommendations and consults. Familiarize yourself with the prices and discounts for the commonly prescribed drugs in the area and become the go-to guy when a doc needs to know where a patient who is strapped for cash can get something for the best price. Find coupons and deals, or co-pay cards. You mentioned asthma and diabetes teaching above, ask the clinic leadership about setting up a system for diabetes, COPD, and asthma "tune-up" visits, where you can use your qualifications and knowledge to easily assess how well-controlled the disease is, deliver teaching on how to improve control, and make adjustments to medications, all possibly within your scope of practice depending on where you're working.