How does getting a seat on a military flight work? Is it even worth my time vs getting a regular flight?

SPC (Join to see) google space available travel. You'll have to call the termnals you plan to use. It's all supposed to be standardized, but here to tell you it ain't. They all have their different application of the rules. Flying alone as an AD SM on leave will up your priority but unless you have time on your hands, you can't depend on it. Some PAX terminals allow you to sign up on line and submit your DA31 to get on the list ahead of time. Then again, some won't. It really is random and capricious. You have to be financially prepared to buy a no notice ticket to get back. OBTW Air India sucks...ask me how I know.

I've taken Space A flights only once from Carson all the way to Guam. Let's just say I almost used up all my leave just waiting for a flight to Guam while in Hawaii. I ended up purchasing a tickets.
Check the AF websites nearest to you, and see where their destination is and how many seats are available. There is an online portion or a form you are supposed to fill out. Also, you will be categorized between all other Space A passengers meaning, if you are just taking regular leave, you will be bottom priority vs someone who is taking emergency leave or someone who is on R&R leave from a combat deployment. Then there is the actual seat availability. If a certain flight will have 4 seats available and you have a family of 5, you're SOL, even if there are seats available. If not, you're stuck and you will have to wait for the next flight which depends. There's also the course of the flight destinations. When I went from Carson, we flew all the way to Maryland, stayed the night for the next flight then we flew all the way to California. We went the opposite direction, which in turn, wasted a whole day.
They don't serve food but I know you do have a chance to buy a boxed lunch for like $5 before hand. So to answer your question if it works, yes. Is it worth it, if you have the time available plus it's virtually free. It's just too time consuming.

Trying to get space on a military flight is "as available" status. Meaning that you have no idea IF or even when a flight might come available. For leave it is far better for you timewise to simply book a civilian flight and be done with it. You know when and where you will depart and can similarly tell that same information of arrival to anyone meeting you on the receiving end. Plus, when scheduling there is sometimes a discount for a round trip returning flight.

Out of a dozen times I have done military space available flights, I have only lucked out timing wise with two of them failing close to the start of my leave.