Social media posts get more traction if they include a graphic or image. You need a project "brand". People notice the image and click on the post. If there's no image - just informational text - they tend to not click on it and not-reshare it. You want as many people to re-share your project as possible.
And of course... what do you want people to do with all these images? Likely you'll need a project page or website that explains what you're looking for and how to submit their images to the project.
This page might be something that Wounded Warriors would host -- or it could be setup elsewhere (but hopefully they'd link to it so that anyone visiting their website for information would find your project site.)
You can also take advantage of the collection capabilities of existing photo sites such as 500px, Flickr, Google+, etc. such that people can post the images to their own page but add them to your group. That way people can join the group and watch the images start to appear. If I'm submitting images to a project, I'd like to be able to watch that project grow. If I submit to a black box -- and someone else presumably does something with these images but I don't see it -- then I'm less likely to be excited about participating in that project.
I actually dislike Facebook for these sorts of things. Facebook has no concept of a worthy cause. I've got a few non-profits which have Facebook pages. Once upon a time, you could get people to "like" your page and anytime you posted something on that page, it would show up in the stream of people who "like" you. Not anymore. TODAY Facebook has it in their mind that there are only two kinds of pages... personal pages that belong to an individual and only a single individual and "everything else". They want to monetize their product and so they sell promotion capabilities to businesses. So if I'm a restaurant and I want to advertise a dinner special, I can pay Facebook to promote my event or page and you pay to promote through based on the area of coverage. A restaurant or small business can pay to promote to just their own town and maybe even the neighboring towns. It's not too expensive. You, on the other hand, want to promote across the entire country. The problem with Facebook is that if you set up a project page there and people "like" your page, they still won't see posts from you because you aren't "paying" to promote. There's a series of settings that users can configure to insist that they "like" a page so much that they want to be notified of every single thing that is posted... but that's not the default and users have to go out of their way to enable it (Facebook makes it less obvious on purposes because if it was too easy then businesses wouldn't need to pay to promote.) Facebook has no concept of a non-profit charity. A non-profit has to pay to promote just like any commercial business would have to pay.
My astronomy club promotes events such as planetarium shows, club meetings, observing nights, and special events via MeetUp.com and a new neighborhood social app called NextDoor.com as well as Facebook and Twitter. We always ask people how they found us. Some people found us by just doing a Google search for something they're interested in and our page shows up ... but we seem to get the most traction from MeetUp and NextDoor... followed by general Google searches that found us. We get the LEAST number of people who found us via Facebook (it almost never happens that anyone found us on Facebook). We also have a Twitter feed and that gets a little traffic.
You're not quite the same because you don't have an event as in "be at this location on this day to participate in the event" -- you have more of a project that will last many months. However... if you are aware of any scheduled veterans events and those event planners think their participants would be interested in having their portraits made then you could create events where you encourage photographers to show up with gear and be prepared to offer portrait shots... or at least encourage photographers to distribute info to the local veterans (e.g. VFW halls, etc.) that the participating photographer would consider it their honor to give back to those who have served by doing a portrait shoot - complementary. Make it clear to the photographers who participate that this is not meant to be a money-making opportunity (but if that veteran or family member has a need for a photographer in the future... now they know someone they can call.)
) Good points, and Derrel, that's a great idea. I hadn't thought of contacting the local community events station, but I will do that.
