  A flag of codes $C_0 \subsetneq C_1 \subsetneq \cdots \subsetneq C_s
\subseteq {\mathbb F}_q^n$ is said to satisfy the {\it isometry-dual property}
if there exists ${\bf x}\in (\mathbb{F}_q^*)^n$ such that the code $C_i$ is
{\bf x}-isometric to the dual code $C_{s-i}^\perp$ for all $i=0,\ldots, s$. For
$P$ and $Q$ rational places in a function field ${\mathcal F}$, we investigate
the existence of isometry-dual flags of codes in the families of two-point
algebraic geometry codes $$C_\mathcal L(D, a_0P+bQ)\subsetneq C_\mathcal L(D,
a_1P+bQ)\subsetneq \dots \subsetneq C_\mathcal L(D, a_sP+bQ),$$ where the
divisor $D$ is the sum of pairwise different rational places of ${\mathcal F}$
and $P, Q$ are not in $\mbox{supp}(D)$. We characterize those sequences in
terms of $b$ for general function fields. We then apply the result to the broad
class of Kummer extensions ${\mathcal F}$ defined by affine equations of the
form $y^m=f(x)$, for $f(x)$ a separable polynomial of degree $r$, where
$\mbox{gcd}(r, m)=1$. For $P$ the rational place at infinity and $Q$ the
rational place associated to one of the roots of $f(x)$, it is shown that the
flag of two-point algebraic geometry codes has the isometry-dual property if
and only if $m$ divides $2b+1$. At the end we illustrate our results by
applying them to two-point codes over several well know function fields.
