Does the Bobby Kennedy Act apply to the position of Vice President?

[Del Tachi]

No, statutes don't override the Constitution (in this case, the 12th Amendment).

However, Clinton would've been unable to win Arkansas in 1996 unless he and Hillary claimed to reside in different states, which would be...awkward.

For a contemporary example, Donald Trump of Florida and Donald Trump Jr of New York could run together with no problem.

Bill could have reigstered to vote in Washington D.C, while Hillary continued to use an Arkansas voting address (and voted absentee).

Problem solved.

Indeed.  Dick Cheney switched his voter registration from TX to WY just weeks before W tapped him for VP

[Del Tachi]

No, statutes don't override the Constitution (in this case, the 12th Amendment).

However, Clinton would've been unable to win Arkansas in 1996 unless he and Hillary claimed to reside in different states, which would be...awkward.

For a contemporary example, Donald Trump of Florida and Donald Trump Jr of New York could run together with no problem.

Donald Trump of New York and Donald Trump Jr of New York could probably run together with no problem already, since NY's 29 electors are extremely unlikely to be pledged to them anyway.