No, you are missing the point.
The "flip" everyone is talking about isn't voting patterns, it is on policy.
The question was "The Democratic Party used to be the party of the south/segregation. What year (or decade) is the point where the two parties flipped places on this issue?"
The policy changed happened in 1964 with the Republican Goldwater campaign:
In the 1964 presidential election, Goldwater ran a conservative campaign that broadly opposed strong action by the federal government. Although he had supported all previous federal civil rights legislation, Goldwater opposed the Civil Rights Act and championed this opposition during the campaign. He believed that this act was an intrusion of the federal government into the affairs of state; and second, that the Act interfered with the rights of private persons to do business, or not, with whomever they chose, even if the choice is based on racial discrimination.
Goldwater's position appealed to white Southern Democrats and Goldwater was the first Republican presidential candidate since Reconstruction to win the electoral votes of the Deep South states (Louisiana, Georgia, Alabama, Mississippi and South Carolina). Outside the South, Goldwater's negative vote on the Civil Rights Act proved devastating to his campaign. The only other state he won was his home one of Arizona and he suffered a landslide defeat. A Lyndon B. Johnson ad called "Confessions of a Republican", which ran in Northern and Western states, associated Goldwater with the Ku Klux Klan. At the same time, Johnson's campaign in the Deep South publicized Goldwater's support for pre-1964 civil rights legislation.[1]
Prior to that the Republican party was mostly supportive of the Civil Rights Act, and afterwards it wasn't. The opposite was true in the Democratic party.
[1] https://en.wikipedia.org/wiki/Southern_strategy