[SalesForce] How to get the Content document Id for file that was just uploaded for a custom object

The trigger can also be written on COntent Version .The content version object has field version Data and that holds data in base 64 encoded format .

https://www.salesforce.com/developer/docs/api/Content/sforce_api_objects_contentversion.htm

You need to put a check to verify if ContentDocumentLink records exist before putting it into final list ContentDocumentList. Logic will be like this.

trigger ContentVersionTrigger on ContentVersion (after insert) {
    if(!TriggerRunOnce.hasAlreadyfired())
    {
        List<user> users = [select user.id, user.Email, user.FirstName, user.LastName, user.profile.name, user.Username, user.IsActive 
        FROM user, user.profile 
        where user.LastName IN ('***','***') and user.IsActive=true];
        Set<Id> contentDocumentIdSet = new Set<Id>();

        for(ContentVersion cv:trigger.new)
        {
            if(cv.ContentDocumentId != null)
            {
                contentDocumentIdSet.add(cv.ContentDocumentId);
            }
        }

        List<ContentDocumentLink> lstContentDocumentlink = [SELECT ContentDocumentId, LINKEDENTITYID 
                                                            FROM ContentDocumentLink WHERE ContentDocumentId IN:contentDocumentIdSet];


        List<ContentDocumentLink> ContentDocumentList = new List<ContentDocumentLink>();


        for(ContentVersion cv:trigger.new)
        {
            system.debug('at 5 '+cv);
            if(cv.ContentDocumentId != null && !lstContentDocumentlink.contains(cv.ContentDocumentId))
            {
                for(user u:users){
                    if(u.Id != cv.OwnerId){
                        ContentDocumentLink cdl = new ContentDocumentLink(ContentDocumentId=cv.ContentDocumentId,LINKEDENTITYID = u.Id,SHARETYPE='C');
                        ContentDocumentList.add(cdl);  
                    }
                }
            }
        }

        insert ContentDocumentList;
        TriggerRunOnce.setAlreadyfired();
    }
}