In the last decade, selectively tuned bio-based polyesters have been increasingly used for their clinical potential in several biomedical applications, such as tissue engineering, wound healing, and drug delivery. With a biomedical application in mind, a flexible polyester was produced by melt polycondensation using the microbial oil residue collected after the distillation of β-farnesene (FDR) produced industrially by genetically modified yeast, Saccharomyces cerevisiae. After characterization, the polyester exhibited elongation up to 150% and presented Tg of −51.2 °C and Tm of 169.8 °C. In vitro degradation revealed a mass loss of about 87% after storage in PBS solution for 11 weeks under accelerated conditions (40 °C, RH = 75%). The water contact angle revealed a hydrophilic character, and biocompatibility with skin cells was demonstrated. 3D and 2D scaffolds were produced by salt-leaching, and a controlled release study at 30 °C was performed with Rhodamine B base (RBB, 3D) and curcumin (CRC, 2D), showing a diffusion-controlled mechanism with about 29.3% of RBB released after 48 h and 50.4% of CRC after 7 h. This polymer offers a sustainable and eco-friendly alternative for the potential use of the controlled release of active principles for wound dressing applications.