What is the significance of the kink in the [A] vs T graph for a 2nd order reaction?
There's no significance to the shape, that's simply how any graph of the form $y = 1/(c+x)$ looks like ($c$ being any constant you like).
Even if the supposed "kink" has some significance, there isn't any significance to the number, especially since the number depends on your system anyway (it's dependent on the value of your rate constant as well as the initial concentration).