The Ketzos haShulchan does not permit laying out poisonous substances, since these are ‘muktze’, (something that is not needed on Shabbat and therefore one is not allowed to use it,) as it is not food. He also does not permit spraying the flies because if one sprays it on the fly and it dies as a result, one has directly killed on Shabbat. Many authorities disagree (like Rav S. Z. Auerbach,) because it is designated for that specific use.
In a case of great need it is permitted to spray the room as long as the windows are open so that the flies can escape.