Here's my 2 cents:
A question like this can mean have different interpretations, and even different interpretations between Fish & Game WCO's. Here in PA I have heard of guys getting fines for things that other WCO's may have not taken objection to. While we might have someone with enough insight into the Arkansas Fish & Game regulations to answer the question, it might best be answered by them.
Why not try to contact them to see what their definition of "single barbless hook" really means?
This way, once you have their official response on it, you have a means to CYA if a WCO would perhaps fine you for not adhering to his interpretation of the rules.
Or take the path of least resistance and make sure you're fishing flies in those special regs areas with one single barbless hook.
FWIW, I'd interpret that as treble or double hooks are not permitted and literally one hook on your fly. But what do I know about fishing regs in Arkansas?
Most of the articulated flies I own and fish with have only one hook on them. While I might use a shank to get the head/body of the fly completed, I cut the hook off so there is only one hook--on the tail.