The largest percentage of pairs with the second term being divisible by the first term is achieved in the case of tuple $(1, 2, \dots, n)$. Indeed, consider an arbitrary tuple of the form $(x+1, x+2, \dots, x+n)$ where

$x > 0$. For any $i$, multiples of $i$ in $(1,2,...,n)$ are every $i$th term starting from the number $i$, multiples of $x+i$ in $(x+1,x+2,...,x+n)$ are every $(x+i)$th term starting from $x+i$. The latter multiples occuring more seldom while the first occurrence being at the same position implies the same or smaller total number.
It is easy to check that the degree of divisibility of $(1,2,3,4,5)$ is $\frac{5}{10}$ and the degree of divisibility of $(1,2,3,4,5,6)$ is $\frac{8}{15}$. By the above, $j(6) > j(5)$.

Calculation shows that the degrees of divisibility of tuples $(1,2,3,4,5)$, $(2,3,4,5,6)$, $(3,4,5,6,7)$ and $(4,5,6,7,8)$ are $\frac{5}{10}$, $\frac{3}{10}$, $\frac{1}{10}$ and $\frac{1}{10}$, respectively. If the first term of a quintuple is 5 or larger then no two terms can divide each other since the largest term is less than twice larger than the least term. Hence $j(5) = \frac{5}{10} = \frac{1}{2}$. As the degree of divisibility of $(1,2,3,4,5,6)$ is $\frac{8}{15}$, we have $j(6) \ge \frac{8}{15} > \frac{1}{2} = j(5)$.