To find/query/SQOL all the Chatter Posts for a specific user in Salesforce, run a SOQL FeedItem object/entity where InsertedById is filtered by the id of the user.

SOQL:

SELECT Id, Body, Status, Type 
FROM FeedItem 
WHERE InsertedById = '<Id of the User>'

Reference Article for additional fields:

https://developer.salesforce.com/docs/atlas.en-us.api.meta/api/sforce_api_objects_feeditem.htm

Output: