You can either use the fuzzy query:
{
"fuzzy" : { "user" : "ki" }
}
Or use the fuzziness
factor in a match
query. Another way to achieve what you want in your example is to use synonyms. With synonyms you can tell elasticsearch to store synonyms to your words along with the original words, e.g. gray will be stored as gray and grey.
Here is a in-depth description of the synonyms: http://www.elasticsearch.org/guide/en/elasticsearch/reference/current/analysis-synonym-tokenfilter.html