This paper presents a flexible and wearable (on-body) dual band antenna operating in two Industrial, Scientific and Medical (ISM) frequency bands. The central frequencies selected are equal to 2.45 GHz and 5.8 GHz. In order to make the antenna suitable for Wireless Body Area Network (WBAN) applications, it is fabricated on a flexible biopolymer called cellulose laurate (CL). The proposed antenna, that has been designed and optimized on ANSYS HFSS, is realized using a process based on copper adhesive tape and laser structuring. The characterization of the antenna in terms of reflection coefficient, gain and radiation patterns shows a good agreement with the simulation data. Compared to state-of-the-art antennas, the investigated solution demonstrates competitive results. The proposed antenna also features stable performance under bending conditions and the estimated specific absorption rate (SAR) is well below the limits defined by international standards. All these results suggest that the proposed antenna is very well suited for potential wearable applications and is a step towards fully green electronics.