The ff.search.yahoo.com server is used for type-ahead search in browsers like Firefox. It's not an API, and I would not recommend developing anything that uses it. (In addition to possible terms of service violations, it may cease working or change at any time.)
As an alternative, you could use Yahoo's YQL service to select from the Search Suggestions search interface.
Here's an example query for the search term "soccer" (which you can try in the YQL console):
select k from yahoo.search.suggestions where command="soccer"
Sample results:
{
"query": {
"count": 10,
"created": "2012-10-21T01:16:15Z",
"lang": "en-US",
"results": {
"s": [
{
"k": "soccernet"
},
{
"k": "soccer games"
},
{
"k": "soccer.com"
},
{
"k": "soccer ball"
},
{
"k": "soccer offices raided"
},
{
"k": "soccer jerseys"
},
{
"k": "soccer shoes"
},
{
"k": "fox soccer channel"
},
{
"k": "world cup soccer"
},
{
"k": "mls soccer"
}
]
}
}
}