Police said in a news release Wednesday Kevin Michael Purfield, 45, was charged with five counts of telephonic harassment and one count of stalking.
Aurora police contacted Portland police detectives in February, requesting assistance in an investigation into unwanted emails, telephone calls and social media posts Purfield allegedly used to contact family members of people killed in the July 20 massacre during a midnight screening of "The Dark Knight Rises."
"None of the contacts were threatening but were unwanted and annoying and Purfield would often use vile language," the Portland police news release said.
"We invited them over if they want to see what it's like to sit at the dinner table without your child," Tom Teves, whose son was killed as he shielded his fiance from gunfire in the movie theater, told KPNX-TV, Phoenix, in a report that aired Wednesday.
Teves said the time "to speak out is before somebody pins your kid down in a movie theater with an assault weapon and then blows his head off."
A spokesman for Flake told the TV station the senator's office was trying to arrange a meeting with the Teves family.
Alex Teves' mother, Caren Teves, made headlines in February when she asked McCain at a town hall meeting in Phoenix about prospects for federal legislation to ban military-style assault weapons.
In his response, McCain said: "I can tell you right now you need some straight talk. That assault weapons ban will not pass the Congress of the United States."
Caren Teves said at the time McCain's response -- which drew applause and cheers from others at the town hall -- was "appalling."