  In this work, we study the higher order Kirchhoff type Choquard equation
$(KC)$ involving a critical exponential non-linearity and singular weights. We
prove the existence of solution to $(KC)$ using Mountain pass Lemma in light of
Moser-Trudinger and singular Adams-Moser inequalities. In the second part of
the paper, using the Nehari manifold technique and minimization over its
suitable subsets, we prove the existence of at least two solutions to the
Kirchhoff type Choquard equation $(\mathcal{P_{\la,M}})$ involving
convex-concave type non-linearity.
