According to the article by K Steinhagen et al, the use of Zika-specific NS1 as the target antigen prevents cross-reactivity with antibodies against other flaviviruses.
The recent multicohort study reveals Zika NS1-based ELISA has “… a combined sensitivity (IgM/IgG) of 100% for RT-PCR-confirmed cases of ZIKV infection at 99.8% specificity. Among suspected ZIKV cases, the combined sensitivity amounted to 89.5%.”
"Cross-reactivity with high-level dengue virus antibodies was not detected"
(K Steinhagen et al, EuroSurveillance 2016 Dec 15;21(50))
Please refer to the article for more information on the study.