Chandra is not thousands of years old.

First, the MTGSalvation wiki is attempting to operate off an older dating system used by Magic's story in the past, claiming the year she was born is 4586 A.R..

Second, Planeswalkers could only live for thousands of years before the Mending. The Mending was an event that changed the nature of the Planeswalker spark, resulting in more mortal and less ageless Planeswalkers.

Third, here is a relevant bit from the recent Magic Story "Homesick":

"Her parents, unless I greatly miss my guess. Twelve years ago, they compelled their daughter—her name was not recorded—to assist in their smuggling operations. I am not familiar with the details, but the girl escaped custody when she manifested dangerous pyromantic abilities. The Nalaars attempted to hide in the countryside. A manhunt brought them to ground in Bunarat, but during the attempt to take them into custody, the village was set ablaze. All three were reported dead by the officer in charge." "Twelve years?" Gideon said, aghast. "But she's only—!" "She would have been a child," Nissa said, softly.