"Certainly, the Kenyan government would not be interested in harming her," said Washington, D.C. immigration lawyer Andres Benach, who regularly takes asylum cases, but is not involved in this case. "So she would have to show that it would be persecution by groups that the Kenyan government is unable or unwilling to control -- maybe al Qaeda-like organizations that operate with a measure of impunity in Kenya."
Convincing a judge that Onyango would face persecution because of her familial relationship with Obama will be hard to prove, Benach said.
Most people who apply for asylum don't receive it because the burden of proof for the feared persecution is that it has at least a 10 percent chance of happening.
"Personal vendettas, random crime, conditions everybody is subjected to, do not support asylum," Benach said.
In 2008, the Department of Justice Executive Office for Immigration Review completed 46,237 asylum cases -- 10,743 of which were granted, 13,199 were denied, and 22,295 were other closures, agency spokeswoman Lauren Alder Reid told ABC News.
Kenyans have made up a relatively small portion of asylum requests over the past 10 years. Of the 343 applications, only 60 were granted asylum.
The Associated Press contributed to this report.