As noble a cause and intentions as Angel Flight is/has, I'd tell them to go pound sand. No one but my financials get my SSN.
You send it to them in an email. Email goes through a chain of servers before being delivered (check the full header sometime). Then some stranger reads the email. Then they enter it into a likely insecure database like an Excel spreadsheet. This protects them from future liability as supporting proof they ran a background check. How many employees/volunteers have access? Then they submit all your info (name, address, SSN) to some other service doing the background check. How many people at the background service have access? Then they save the results in another or the same likely insecure database, again for liability reasons. In the end, at least dozens of people will have or have had access to your SSN.
Ever been a victim of true identity theft? And I don't mean bogus charges to a credit card. Nothing is worth unraveling from a car loan or mortgage you did not initiate.