The points I have edged my inside pocket with appear to be called prairie points and are the type that can be nested as described in this McCalls post. I saw this idea somewhere else and it was described as a Hong Kong pocket or something similar, so is something traditionally found in tailored garments. Mine is a lot clunkier and less delicate than the example I have seen because I wanted it to look like teeth to scare my children (naturally), but you could make this look far more delicate with smaller nested points.
To start, there was no pattern for an inside pocket, so I just free hand cut into the fabric two pocket pieces. It is a rectangle big enough to store a phone and the extra bit on the side is big enough for my hand to fit in and out of. That extra bit is 1.5cm wider than the bottom edge.
I folded back the edge flap by 1.5 cm (wrong sides together) and pressed along this line on both pocket pieces.
I then marked with chalk the end of the pocket opening so I know where to start sewing when I come to make the pocket up. I used a seam allowance of 1cm for the pocket seams.
I cut a long strip of the lining fabric which measured 6cm wide, but you can alter this to make smaller or larger triangles.
I pressed it along the length with wrong sides together and then chopped it up into short lengths. They look approximately 6cm long, but I don't think you need to be terribly accurate with this method. The McCalls link I mentioned above is far more methodical if you want to work to a more precise formula.
My pocket is on the left hand of my coat, so I sewed the triangles to the pocket lining piece with the extra flap on the right hand side (if the right side of the fabric is facing up).
I used the pressed line on the pocket lining as my stitch guide and just kept adding the points as I got to the end of the last one so they are butt up next to each other. I just went by eye to make sure the height of the points are the same, but you could easily draw a chalk line for accuracy.
Important - Make sure the points remain within the seam allowance of the pocket bag!
Yet another example of my non-methodical approach to this technique is the excess from the points in the picture below. Just trim these down in line with the pocket lining edge.
Make the pocket up! Sew the two pieces with right sides together and with the points pointing inside the pocket. Don't go beyond the stitch line along the pocket opening when joining your pocket pieces together. FYI - The seam below at the bottom of the pocket opening is an 'L' shaped seam if you are planning to cut the same shape pocket as me.
Pin the pocket bag to your coat lining centre front edge and sew in place. It is the edge with the points on you are attaching to the lining (although you could sew the points to the coat if you prefer).
Next flip the pocket back around to the wrong side of the lining and that's pretty much it!
When you hand sew your lining into your coat you can also sew the remaining edge of your pocket down.
I was just making it up as I went along to try an idea out, but you can iron out any kinks and make a much nicer job of it if you have a go!