Read the excerpt from The People Could Fly

So [the alligators] all be quiet. Until the fire flare real high and close. . . . The gators swink close down but it don't do them no good. They got to move. The hot fire is real up now. It blister they tails and they snouts. And the gators are runnin away.

Based on the clues in the excerpt, the word swink most likely means

“walk.”
“leap.”
“crouch.”
“tumble.”