Statement (A): The stability initially increases with bitumen content, reaches a maximum, and then decreases with further increase in bitumen content. Therefore, Statement (A) is False.
Statement (B): With an increase in bitumen content, the flow increases monotonically because the more bitumen there is, the more it flows and spreads in the mix. Hence, Statement (B) is True.
Statement (C): The air voids ($V_A$) decrease initially with increasing bitumen content, reach a minimum, and then start increasing. Hence, Statement (C) is False.
Statement (D): The voids filled with bitumen ($V_{FB}$) increases monotonically with an increase in bitumen content, as more bitumen fills the voids in the mixture. Hence, Statement (D) is True.
\[
\boxed{\text{Correct Statements: (B) and (D)}}
\]