FAD (fatty acid desaturase) and SAD (stearoyl-ACP desaturase) genes play key roles in the synthesis of fatty acids (FA) and determination of oil composition in flax (Linum usitatissimum L.). We searched for FAD and SAD genes in the most widely used flax genome of the variety CDC Bethune and three available long-read assembled flax genomes—YY5, 3896, and Atlant. We identified fifteen FAD2, six FAD3, and four SAD genes. Of all the identified genes, 24 were present in duplicated pairs. In most cases, two genes from a pair differed by a significant number of gene-specific SNPs (single nucleotide polymorphisms) or even InDels (insertions/deletions), except for FAD2a-1 and FAD2a-2, where only seven SNPs distinguished these genes. Errors were detected in the FAD2a-1, FAD2a-2, FAD3c-1, and FAD3d-2 sequences in the CDC Bethune genome assembly but not in the long-read genome assemblies. Expression analysis of the available transcriptomic data for different flax organs/tissues revealed that FAD2a-1, FAD2a-2, FAD3a, FAD3b, SAD3-1, and SAD3-2 were specifically expressed in embryos/seeds/capsules and could play a crucial role in the synthesis of FA in flax seeds. In contrast, FAD2b-1, FAD2b-2, SAD2-1, and SAD2-2 were highly expressed in all analyzed organs/tissues and could be involved in FA synthesis in whole flax plants. FAD2c-2, FAD2d-1, FAD3c-1, FAD3c-2, FAD3d-1, FAD3d-2, SAD3-1, and SAD3-2 showed differential expression under stress conditions—Fusarium oxysporum infection and drought. The obtained results are essential for research on molecular mechanisms of fatty acid synthesis, FAD and SAD editing, and marker-assisted and genomic selection for breeding flax varieties with a determined fatty acid composition of oil.