I am doing a research project involving calculating k-mer frequencies and I am wondering if there is any standard file format for storing k-mer counts.
Not as far as I am aware. The Ray assembler used to (and possibly still does) store the kmers as FASTA files where the header was the count of the sequence, which I thought was a pretty neat bastardisation of the FASTA file format. It looks like this format is also used by Jellyfish when reporting kmer frequencies by the
dump command (but its default output format is a custom binary format):
The dump subcommand outputs a list of all the k-mers in the file associated with their count. By default, the output is in FASTA format, where the header line contains the count of the k-mer and the sequence part is the sequence of the k-mer. This format has the advantage that the output contains the sequence of k-mers and can be directly fed into another program expecting the very common FASTA format. A more convenient column format (for human beings) is selected with the -c switch.
Jellyfish changed their internal format between v1 and v2 (both not FASTA), because they changed to doing counts based on bloom filters. Jellyfish2 has an optional two-pass method that sets up a bloom filter intermediate file to record kmers, and multiple different final reporting formats.
Khmer also uses bloom filters, but in a slightly different way. It also has been extended to be useful for partitioning and comparing datasets.