How to install door security guard on metal door jamb?
Before I start - this is a simple task but it's not as simple as it might seem at first glance.  

I would mount this with flat head machine screws.  I would take that lock to the hardware store and see what size fits right in the countersinks (the tapered part).  It might be say a size 8 machine screw.  Most of are threaded with so that there are 32 threads per inch (the thread pitch).  

You'll need to drill a hole the exact right size for the screw, and cut or form or "tap" matching threads in the hole so the threads bite.  The easy way to do this is buy a combination drill bit and tap for the size screw you selected, for example this 8-32 drill-tap:  



You can probably see how this works, you drill the hole through the metal first, then you keep going and tap the threads with the same bit.  

I would advise buying two of these drill-taps because they break easily, and practice on some thin scrap metal before you try it on your door frame.    

The fine points of drilling and tapping are way beyond this answer but I'll say you want to drill slow with firm pressure, then tap with a little less pressure and the minimum torque to cut the threads.  

It's always good to lubricate the drill bit when drilling metal but it's especially important with a tap.  There is special tapping lubricant made just for this job but a dab of petroleum jelly on the bit will work fine.  

When you put the hardware on the door frame to mark the holes, be sure to hold it steady and make sure it's in the right spot.  It's also important to make a small dimple in the metal so the tip of the drill bit stays in the exact right spot.  The usual tool for this is a center punch but a large nail will work in a pinch.  Just place the point carefully and rap it with a hammer.  Be as precise as possible!  

Again, this can be very quick and easy if all goes well, but it's very possible it won't.  If the tap breaks off in the hole on the door, you're going to have a headache.  

I'd also mount the bracket on the metal first, THEN mount the part that goes on the door.  I say this because if anything goes wrong mounting it on the door, you may have to move it up or down a bit.