In which Act and Scene in King Lear does Edgar run away?
Edgar is convinced by Edmund in Act I, Scene ii that their father is so enraged at him (Edgar) that his life is in danger. At this, Edgar flies to the heath, disguised as Poor Tom. Edmund has warned him to hide out until their father's wrath cools.
There are a few interesting things to point out about this exchange. First, Edgar takes Edmund's word, even when Edmund can point to no specific event or action committed by Edgar that would have enraged their father.
Edgar does suggest that "some villain hath done me wrong." Pointing out to Edmund (the guy who actually did do him wrong) that he suspects that he was bad mouthed by someone. Edmund actually agrees with him, "That's my fear." All the while, it is Edmund who has displaced Edgar in their father's affections, in an attempt to be named heir to Gloucester's fortune and title.
This exchange is quite short, coming at the end of a long scene and hastily concluded. Edgar shows up again in Act II, Scene iii, when he reappears as Poor Tom.