Updated July 2021
I'm glad to hear you are interested in USAA!
You can invest in USAA as a company, but maybe not like you are thinking. USAA was formed in 1922 by Army Officers, and remains a privately owned, member organization. USAA's stock does not trade publically, so is unavailable for you to buy on the open market. However, there are a couple of ways our members receive benefits back. Members can qualify for multi-product discounts on property and casualty insurance if they use multiple products, you also have access to advice guidance and tools, and some auto insurance policyholders receive dividend payments that can help to reduce their premium. These payments made back to the membership are authorized by the USAA Board of directors based on how the company performs, how much the member pays in insurance premium, and other factors.
You can "invest" in the company simply by doing business with USAA. Every product and service you utilize with USAA helps make the company stronger, which then gets distributed back to members in the form of competitive products & services, the above mentioned policy holder payment, reduced fees, and many services that don't directly cost you anything. USAA also supports (in this writer's humble opinion) world class employees and keeps significant financial reserves so that when that financial strength is needed by you, USAA is there to fulfill our promises.
I hope this helps!