Its about 11% in this study.
https://www.hudexchange.info/resources/documents/2015-AHAR-Part-1.pdf
About 7% of the U.S. population is made up of veterans. So the percentage of veterans that are homeless closely corresponds to the percentage of veterans in the population. It is slightly higher, but not by much. Its still a tragedy, of course, that anyone in the U.S. is homeless.
It would seem that the Department of Veteran Affairs would disagree with your numbers.
The U.S. Department of Veterans Affairs (VA) says the nation's homeless veterans are mostly males (four percent are females). The vast majority is single, most come from poor, disadvantaged communities, 45 percent suffer from mental illness, and half have substance abuse problems. America痴 homeless veterans have served in World War II, Korean War, Cold War, Vietnam War, Grenada, Panama, Lebanon, Operation Enduring Freedom (Afghanistan), Operation Iraqi Freedom, or the military痴 anti-drug cultivation efforts in South America. 47 per cent of homeless veterans served during the Vietnam Era. More than 67 per cent served our country for at least three years and 33 per cent were stationed in a war zone.
Here are some statistics concerning the veterans homeless [2]:
23% of homeless population are veterans
33% of male homeless population are veterans
47% Vietnam Era
17% post-Vietnam
15% pre-Vietnam
67% served three or more years
33% stationed in war zone
25% have used VA Homeless Services
85% completed high school/GED, compared to 56% of non-veterans
89% received Honorable Discharge
79% reside in central cities
16% reside in suburban areas
5% reside in rural areas
76% experience alcohol, drug, or mental health problems
46% white males compared to 34% non-veterans
46% age 45 or older compared to 20% non-veterans
Female homeless veterans represent an estimated 3% of homeless veterans. They are more likely than male homeless veterans to be married and to suffer serious psychiatric illness, but less likely to be employed and to suffer from addiction disorders. Comparisons of homeless female veterans and other homeless women have found no differences in rates of mental illness or addictions.