Solution:

The answer is (C). Let us observe that we have two distinct cases depending on whether the statement "Everyone who declares they will vote for Flavia is a knave" is true or false:

- if the statement is true, then everyone who made it (that is, the $3000$ people who declared they would vote for Carla) are knights; therefore, these $3000$ people will actually vote for Carla. On the other hand, since the statement is true, we know that everyone who declared they would vote for Flavia is a knave, so they were lying during that declaration and will therefore vote for Carla. So in this case all the inhabitants of the island will vote for Carla, the result of the election will be $5000$ to $0$, and the margin of votes for the winner (Carla) will be $5000$.

- if the statement is false, then everyone who made it (that is, the $3000$ people who declared they would vote for Carla) are knaves and, therefore, will vote for Flavia.

Let $n$ (with $n \leq 2000$) be the number of knights who declared they would vote for Flavia (since in this case the above statement is false, we have $n \geq 1$): among these $2000$ people, $n$ will vote for Flavia (because they were telling the truth when declaring who they would vote for) and $2000 - n$ will vote for Carla (since they are knaves, they were lying when declaring who they would vote for). We thus obtain that Carla receives in total $2000-n$ votes, while Flavia receives $3000+n$. In this case the winner (Flavia) will have
$$(3000+n)-(2000-n)=1000+2n$$
votes of margin. Since $1 \leq n \leq 2000$, the margin of votes is between $1002$ and $5000$.

Since the problem asks for the minimum number of margin votes that the winner will have, the answer is $1002$.