How to search in field collection item?
As say in Search interface the search system already indexes all visible output of a node; i.e., everything displayed normally by hook_view() and hook_node_view().

You can activate and configure in the display settings of your content type the custom display "Search index" than will be used for indexing.

If this doesn't works in you case, you can implement hook_node_update_index to add any information you want on the node before is indexed.