In this Letter, we propose and experimentally demonstrate fiber Bragg grating (FBG) fabrication in a flexible and stretchable coreless polymer optical fiber. The flexible polymer optical fiber is prepared with polydimethylsiloxane (PDMS). Femtosecond laser direct writing and slit beam shaping are used to form periodic grating structures in the fiber. The fabricated FBG exhibits a large strain measurement range and a blueshift response to temperature. Moreover, it offers low humidity sensitivity due to its low permeability toward water vapor. Taking advantage of the unique sensing performances of the PDMS fiber, the proposed FBG has considerable advantages over the traditional silica FBG devices for strain and temperature sensing.