Roger's point that multiple selective forces (over a loooooonng time) play roles in current body configurations is a good one. Certainly clinger types are found in a variety of flow and substrate types. But your specific question has certainly been looked at.
I did read something about this a bit ago. As I understand it, the bottom line was that such inverts are not flattened to live in the viscous layer (which is very thin indeed less than 1mm at best and often measured in angstroms) but instead have body morphologies that serve life in complex flows. Here's some of it:
“A growing larva initially is subject to friction drag, but subsequently experiences mainly pressure drag. This analysis implies that animals might be expected to be more rotund when small and become more streamlined as they grow. Since this does not appear to be true, either the analysis is flawed or body shape is constrained by other agents of selection. … Although each of these laboratory studies has its limitations, collectively they undermine the idea that animals on substrate surfaces routinely find shelter from current within a viscous sublayer.”
“Many invertebrate taxa, including those with flattened shape that has long been viewed as an adaptation to dwell within the viscous sublayer, in fact experience complex flows and relatively high shear. For these organisms, size and shape are important mainly because they influence the ratio of inertial to viscous forces that the organism experiences, and not because of (any need for) sheltering from the current.”
-from “Stream Ecology” by David Allan.
-from Statzner and Holm, 1982.
This diagram shows that flow forces are directed at a certain point of the carapace, and that some turbulence is likely at peripheral, esp downstream areas. The body looks like a hydrofoil (same as an aerofoil) complete with canards to regulate turbulence.
Another use for the flattened shape that I’ve observed (many times) and never heard discussed elsewhere is that flattened species that live in strong currents (some clinger mays and stones) can swim very effectively. They appear to tuck the head using the body, and likely the legs, like a diving plane. They also use their flattened legs as paddles, rapidly fluttering them to swim. They are effective in current and can reach bottom very quickly, almost a vertical descent.