Drill Bit Breaking Through

First of all, I have no former training in machining but what I would do is get a scrap piece of cast iron, clamp it very tight on the bottom side of were the hole will be. Then drill it as normal, the scrap piece clamped to it will make the bit not grab as much breaking through.
 
As mentioned above a twist drill when passing through the far side of the material will often corkscrew in with unpleasant results, free machining brass will do this quite easily and either pull the spindle down, rip the part from the chuck/vice or pull the drill from the chuck or collet.

If at all possible powerfeed with a good deal of drag on the spindle movement, if not practical drill through the part into another underlying piece of scrap so that the twist drill can not run away.
 
Drill down till it just starts to break through, then change to a flat bottom drill.
 
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