FMSD-TTS is a few-shot, multi-speaker, multi-dialect text-to-speech framework proposed to address the challenge of low-resource languages lacking parallel speech corpora for the three major Tibetan dialects (U-Tsang, Amdo, and Kham). It synthesizes parallel dialect speech using limited reference audio and explicit dialect labels. It captures subtle acoustic and linguistic variations between dialects while preserving speaker identity through a speaker-dialect fusion module and a dialect-specific dynamic routing network (DSDR-Net). Objective and subjective evaluations demonstrate significant improvements in dialect expressivity and speaker similarity compared to baseline models. Furthermore, the quality and usability of the synthesized speech are verified through a challenging speech-to-speech dialect conversion task. Key contributions include the implementation of a few-shot Tibetan multi-dialect speech synthesis system, the release of a large-scale synthetic Tibetan speech corpus generated by FMSD-TTS, and an open-source evaluation tool for standardized evaluation of speaker similarity, dialect consistency, and audio quality.