When doing antioxidant assays (plants), would one need to generate a standard curve for the specific assay?

Yes, you need to prepare a standard curve using a standard antioxidant compound like ascorbic acid. 

Yes, you have to prepare standard curve

Thank you 

I think each stress treatment has a control. So comparing the contents with the corresponding control will do. And, if you are doing the expriments at the same time and using the same  laboratory reagent , a standard curve for each enzyme would be OK. But if you do your experiments at different times, you will need new standard curves. Because some reagents are not stable and they can not be used after some time. And the newly prepared solution might not be exactly the same as the reagents used before even with the same formula.

Yes, For each antioxidant assay, you need to perform a probable standard curve every time of measurement. you need to use freshly prepared reagent every time in order to have fair comparison and results.