Flax (Linum usitatissimum L.) is attacked by numerous devastating fungal pathogens, including Colletotrichum lini, Aureobasidium pullulans, and Fusarium verticillioides (Fusarium moniliforme). The effective control of flax diseases follows the paradigm of extensive molecular research on pathogenicity. However, such studies require quality genome sequences of the studied organisms. This article reports on the approaches to assembling a high-quality fungal genome from the Oxford Nanopore Technologies data. We sequenced the genomes of C. lini, A. pullulans, and F. verticillioides (F. moniliforme) and received different volumes of sequencing data: 1.7 Gb, 3.9 Gb, and 11.1 Gb, respectively. To obtain the optimal genome sequences, we studied the effect of input data quality and genome coverage on assembly statistics and tested the performance of different assembling and polishing software. For C. lini, the most contiguous and complete assembly was obtained by the Flye assembler and the Homopolish polisher. The genome coverage had more effect than data quality on assembly statistics, likely due to the relatively low amount of sequencing data obtained for C. lini. The final assembly was 53.4 Mb long and 96.4% complete (according to the glomerellales_odb10 BUSCO dataset), consisted of 42 contigs, and had an N50 of 4.4 Mb. For A. pullulans and F. verticillioides (F. moniliforme), the best assemblies were produced by Canu–Medaka and Canu–Homopolish, respectively. The final assembly of A. pullulans had a length of 29.5 Mb, 99.4% completeness (dothideomycetes_odb10), an N50 of 2.4 Mb and consisted of 32 contigs. F. verticillioides (F. moniliforme) assembly was 44.1 Mb long, 97.8% complete (hypocreales_odb10), consisted of 54 contigs, and had an N50 of 4.4 Mb. The obtained results can serve as a guideline for assembling a de novo genome of a fungus. In addition, our data can be used in genomic studies of fungal pathogens or plant–pathogen interactions and assist in the management of flax diseases.