I've found that when working with recycled t-shirts for diaper fabric, you can substitute 2 layers of t-shirt cotton for any one layer of fleece, french terry, or velour. You do not need a special pattern for working with recycled fabrics - any of the existing diaper patterns can be used, including AIO patterns. So, for example, if I were using the VB AIO pattern, I would cut the PUL layer as usual, and then I'd cut the rest of the layers out of t-shirts rather than birdseye, keeping the layer counts the same (because a layer of jersey equals a layer of birdseye, roughly).
Keep an eye on the suggested fabric type in each pattern - does it want you to use wovens or knits? Sometimes it will matter - more often it will make a difference if you substitute a woven for a knit, and not the other way around. (Wovens are more stable, and the pattern may rely on the give of a knit fabric to allow for an optimal size-range.)