Aggregate nearest neighbor (Ann) query in both the euclidean space and road networks has been extensively studied, and the flexible aggregate nearest neighbor (Fann) problem further generalizes Ann by introducing an extra flexibility parameter $\phi$ that ranges in $(0, 1]$. In this article, we focus on Fann on road networks, denoted as Fann$_\mathcal {R}$, and its keyword-aware variant, denoted as KFann$_\mathcal {R}$. To solve these problems, we propose a series of universal (i.e., suitable for both max and sum) algorithms, including a Dijkstra-based algorithm that enumerates $P$ instead of $\phi |Q|$-combinations of $Q$, a queue-based approach that processes data points from-near-to-far, and a framework that combines incremental euclidean restriction (IER) and $k$NN. We also propose a specific exact solution to max-Fann$_\mathcal {R}$ and a constant-factor ratio approximate solution to sum-Fann$_\mathcal {R}$. These specific algorithms are easy to implement and can achieve excellent performance in some scenarios. Besides, we further extend this problem to top-$k$ and multiple Fann$_\mathcal {R}$ (resp., KFann$_\mathcal {R}$) queries. We conduct a comprehensive experimental evaluation for the proposed algorithms on real datasets to demonstrate their superior efficiency and high quality.