These are two great texts to compare and contrast, and I have included links to the study guides on enotes for both of them below to help you in your analysis.
To my mind, the texts can be compared most obviously through their examination of the capacity of humans to commit acts of evil. Both texts show a gradual descent of Macbeth and then Jack and the boys into ever greater acts of bloody savagery. Evil is clearly a major theme, and in particular how it appears to be something of a cumulative process, for once the characters start committing evil acts, the evil escalates.
Secondly, I would want to compare the nature of power and how ambition or pride causes us to fight to have it. Clearly the struggles between Jack and Ralph for the leadership of the boys is mirrored in Macbeth's manipulation of others to maintain his power.
Where the two texts are different is in the ending. Macbeth is bestowed with a curious dignity at the play's end, so that we do genuinely feel sympathy for him to a certain extent, and we admire his bravery as he faces his doom. We feel no such admiration for the boys, however, whose bloody acts are curtailed by the serendipitous arrival of the naval officers.
Secondly, a major theme in Lord of the Flies is how the removal of the trappings of civilisation causes us to show our true savage nature. This is of course not the case in Macbeth, where malign forces (the witches) are shown to have an influence over us.
Hope this gives you a few ideas to get you started. Good luck!