We introduce Flexible Representative Democracy (FRD), a novel hybrid of Representative Democracy (RD) and Direct Democracy (DD), in which voters can alter the issue-dependent weights of a set of elected representatives. In line with the literature on Interactive Democracy, our model allows the voters to actively determine the degree to which the system is direct versus representative. However, unlike Liquid Democracy, FRD uses strictly non-transitive delegations, making delegation cycles impossible, preserving privacy and anonymity, and maintaining a fixed set of accountable elected representatives. We present FRD and analyze it using a computational approach with issues that are independent, binary, and symmetric; we compare the outcomes of various democratic systems using Direct Democracy with majority voting and full participation as an ideal baseline. We find through theoretical and empirical analysis that FRD can yield significant improvements over RD for emulating DD with full participation.