As you are processing data in batch so you will have volume data to send to the external system as well. so I would suggest you call another batch in finish() method your batch.

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global class CalloutsFromBatchExample implements Database.Batchable<SObject>,Database.AllowsCallouts,Database.stateful{

    public Boolean chainAnotherbatch = true;

    public void OwnLocalBatchClass(){
    }   

    public Iterable<SObject> start(Database.BatchableContext bc){

        Integer totalCallouts = Limits.getLimitCallouts();

        for(Integer i = 0;i<totalCallouts;i++){
            //Make the callout
            //Build the scope object
            //Have a if condition to set the chainAnotherbatch boolean to true or false.            
        }
        return scope;
    }

    public void execute(Database.BatchableContext bc, List<Sobject> scope){
            Database.insert(scope); 
    }

    public void finish(Database.BatchableContext bc){
        if(chainAnotherbatch){
            Database.executeBatch(new CalloutsFromBatchExample(),1000);
        }else{
            System.debug('Start method signalled that no need to chain another batch another batch job ');
        }
    }
}
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https://salesforce.stackexchange.com/questions/88890/calling-batch-from-finish-of-same-batch-job

Please mark it best if it helps you. Thanks.