You can find the Affinity Photo displace filter via the distort section. It requires a layer or an image or text or shape etc or pattern, basically you can use the feature with a lot of different parts of the application
You can modify the pixels either using the loaded image (in the case of this application, it has to be a PNG file) as well as using the under lying layers (which can be any pixel information). Apply it and you will see the artwork distorted using the gray scale information from those sources. There is only strength and load map from file as well as load map from layers (and that is the key thing, layers) below / beneath. It is more like a glass effect than the Photoshop similar named tool.
Create something in the layer below and apply effects etc to the artwork. Go to the main layer and then select the effect via the distort menu and click layers beneath option and you should see the layer distort based on the strength setting and the gray scale values of the layers. As they can be anything such as a pattern layer, gradients etc, millions of great designs can be created. It should be noted that you have to click it each and every time to load the layer and apply using it
You can also load map from a file (note that you can't have both at the same time). The file format to select is PNG and it is a gray scale file. You can also scale so it matches the current document or not.
You can apply it to channels, you can go the channels panel (view menu) and select the red channel and distort that with one image, go to the green channel and then distort it with a different image or set of layers etc
You can use the load from file and load the image that is currently being used. You can use file open and then go to the command and use the load map from file and select the same file. At 0% there is no change, it be odd if there was but you can push it up or down to a minimum of -512 and maximum of 512 to create a very unusual look depending on the underlying image. As with all, you can also re-apply using the repeat feature and repeat though the result generally just seems to be a more misty version each and every time. You can also combine it with the fade command found in the layer menu and set the repeat fade to say linear burn for some fascinating darkening effects with the map. You can also modify the original image with other effects such as blurs etc and then apply the command to that and combine that also with the fade and blending modes to create some very odd combinations as you end up bringing back the original but in a more sketched loose form / ghostly look.
You can apply it with itself or any other image and then go to the layer menu and apply the fade with a blending mode such as linear burn or lighten etc or change the opacity and this also can be re-applied by the repeat command. So if you use linear burn, you end up creating a more intense darkened image in seconds using the repeat fade
You can also re-apply the effect multiple times with the same image file (or different ones as well as the original image) but each time, use a different setting. Perhaps bounce between 200px and -200px each and every time to create a much more interesting outline around the design.
You can also add a selection using any of the tools such as the rectangular marquee to limit the range of the effect
Text can be used as an interesting source, any text such as artistic as well as frame. You can also use it with a map file and distort (or turn the text into noise) that with the panel. Set the value to fairly low and the text will still be unreadable, set it high and you will see the original image more and more.
You can use the effect with the image itself as well as variants of the image or perhaps use a variant of the image with the map being the image, all kinds of combinations can be used to create some truly wonderful distiorted / sketch / warped images. Open an image and then go to the menu command and use the load file command and select the same image. Change the setting either positive or negative to see the effect. You can also use the repeat feature multiple times with the same photo.. You can also create some variants from the image such as apply a motion blur and then save that as a file and then load that as the file instead to create streaks across the image. You can also load the variant and then apply the map using the original and this creates a sort of glass emboss effect.