Answer
$\approx 0.36c$
Work Step by Step
We have here 2 frames of reference, $\rm S$, and $ S'$ for Sun, and the spaceship rocket respectively.
Where, in $\rm S$ frame, $v_R=0.8c$ ($_R$ for rocket), and $v_F=0.9c$ ($_F$ for flare).
Now we can use the Using the Lorentz transformation equation for velocity to find $v_F'$
$$v_F'=\dfrac{v_F-v_R}{1-\frac{v_R\;v_F}{c^2}}$$
Plug the known;
$$v_F'=\dfrac{0.9 c-0.8 c}{1-\frac{(0.9)(0.8)c^2}{c^2}}$$
$$v_F'=\color{red}{\bf 0.357}c$$
Thus, the flare approaches the rocket at a speed of $\approx 0.36c$.
