Flip Sprite using the SpriteRenderer component
If you need people to review your code you have to give a complete bunch of working code. 
Here, we can only make assumptions about how what you show interoperate with what you don't show.

Your movementDirection..x and movementDirection..y can only be -1, 0, 1. Correct?
So, why using floats instead of ints ? Or even better, an enum, per example:

enum Movement
{
    Backward = -1,
    None = 0,
    Forward = 1      
};


You only need flipping sprite if movements are negatives (for each axis). That's right?

Why just don't test for backwarding movement and set flipX to false otherwise (same for Y).

void Update()
{   
    flipX = (movementDirection.x == Movement.Backward);
    flipY = (movementDirection.y == Movement.Backward);

    spriteRenderer.flipX = flipX;
    spriteRenderer.flipY = flipY;
}


Edit:
That's in case of neutral fixed states (Movement.None never flipped).
If when no movement you want to keep the last flipped states you still want two statement by axis.

void Update()
{   
    if  (movementDirection.x != Movement.None)
        flipX = (movementDirection.x == Movement.Backward);
    if  (movementDirection.y != Movement.None)
        flipY = (movementDirection.y == Movement.Backward);

    spriteRenderer.flipX = flipX;
    spriteRenderer.flipY = flipY;
}


Edit 2:

For completeness, if you really want to minimize statements, you can use Convert, but i dont think it will improve performances :

void Update()
{   
    if  (movementDirection.x != Movement.None)
        flipX = Convert.ToBoolean(movementDirection.x - 1);
    if  (movementDirection.y != Movement.None)
        flipY = Convert.ToBoolean(movementDirection.y - 1);

    spriteRenderer.flipX = flipX;
    spriteRenderer.flipY = flipY;
}