The pinch punch filter for Affinity Photo can be found in the distort category of the filters menu.
Set the pinch by going to -100 and 100 for the punch and anything in between. You can modify the radius, make subtle changes with a low value or a large distortion with the max of 1024. You can also interactively select the origin position. Most of the features of the application can be set beyond their limits, for some weird reason, this one can't.
It is a wonderful distort tool that can be used once or multiple times to great effects. It can be used with images as well as resources / presets such as patterns and brushes and fonts / EPS designs
It can be used with selections and will distort only the area in the selection. You can add all kinds of selections and use it on those
You can also use it on layers, so you can duplicate the current layer and re-size and then add the effect to create all kinds of weird distortions.
You can also apply it to pattern layers as well as rasterized pattern layers. The best way to use the patterns is to use it with mirror setting as ON and then apply the effect to the bounding box or outside of that region.
Also shapes created via the shapes tools as well as with artistic and frame text.
You can use the repeat feature at the top of the menu to apply the effect again and again. As the limits for this effect are quite low, you may find this repeat feature useful if you want to extend beyond the set radius. If you want to modify the original position then you will just have to re-apply the effect instead so you can set a different origin.
You can fade the effect via the layer menu and fade command which means you can combine a blending mode and opacity to change the end result.
It also comes with a live layer effect which works the same but works with the added feature of being a non destructive effect and can be removed but it can also be quickly added to any layer and the effect can be altered at any point by double clicking the entry in the layer's panel
Go to the view menu and studio and channels and select the red channel and apply the effect with one set of settings and particular origin, then go to the green channel and run it again with a different origin and different radius etc. Again with the blue. You can also do this if you are working with a pattern layer though it is only applied to the small pattern tile. For it to work well, you will have to turn the mirror on in the top left.