I am in the process of creating biological key software tool for use on android devices. I would like to know if there are any established file formats for storing biological key data.
If you mean some thing like .doc .txt .rar or etc. I think there is no special bioinformatics file formats like that, for example NCBI, EMBL, Expasy and others use this common formats in transfering sequence data. BUT there is some thing called file format for introducing data to this data banks for example FASTA file format:
As you see, a sequence in FASTA format begins with a single-line description, followed by lines of sequence data. The description line is distinguished from the sequence data by a greater-than (">") symbol in the first column. The word following the ">" symbol is the identifier of the sequence, and the rest of the line is the description (both are optional). There should be no space between the ">" and the first letter of the identifier. It is recommended that all lines of text be shorter than 80 characters. The sequence ends if another line starting with a ">" appears; this indicates the start of another sequence. you can learn more things about these bioinformatical formats here and here.
I searched a bit and could not find any such format, but I am not a specialist in taxonomy.
From what I understand, the structure you want is that of either a tree or a DAG (Directed Acyclic Graph). Both are straightforward to store in a variety of formats.
One possibility is to use a format similar to other biological data that has a similar data structure. For example, Gene Ontology is a widely used dataset that has the structure of a DAG and has a number of formats including XML listing the parents and additional data of each node in the graph. See here for their formats.