For Affinity Photo distorted text brush strokes, the first step is to create the letters and that is via the artistic or frame text via the tools panel. You can create all kinds of designs, you can choose any fonts and sizes and colors and perhaps have multiple blocks.
You can merge them all together to form a pixel layer or just goto the layer menu and use rasterize.
Once you have your pixel layer, goto the filter menu and blur and add a Gaussian blur or any number of other effects and then also use the distort category and deform. You can create all kinds of weird and wonderful distorted and warped artwork. There are also many other fillers available such as twirl, spherize etc.
Deform,
Gaussian,
Go to the brushes panel (view menu and studio) and then goto the right side menu and create brush from selection (bottom of the menu commands).
You can then double click the brushes entry and change the settings for the dynamics of scattering and rotation and hue / saturation etc as well as the spacing such as using with random settings as well as pressure settings if you are using an art pad and pen. You can tweak the preset in countless ways and apply the stroke via the paint tools as well as use the preview to show the changes to the settings.