Flax is a flowering plant cultivated for its oil and contains various unsaturated fatty acids. Linseed oil is known as the “deep-sea fish oil” of plants, and is beneficial to brain and blood lipids, among other positive effects. Long non-coding RNAs (lncRNAs) play an important role in plant growth and development. There are not many studies assessing how lncRNAs are related to the fatty acid synthesis of flax. The relative oil contents of the seeds of the variety Heiya NO.14 (for fiber) and the variety Macbeth (for oil) were determined at 5 day, 10 day, 20 day, and 30 day after flowering. We found that 10–20 day is an important period for ALA accumulation in the Macbeth variety. The strand-specific transcriptome data were analyzed at these four time points, and a series of lncRNAs related to flax seed development were screened. A competing endogenous RNA (ceRNA) network was constructed and the accuracy of the network was verified using qRT-PCR. MSTRG.20631.1 could act with miR156 on the same target, squamosa promoter-binding-like protein (SPL), to influence fatty acid biosynthesis through a gluconeogenesis-related pathway during flax seed development. This study provides a theoretical basis for future studies assessing the potential functions of lncRNAs during seed development.