There is nothing wrong with the eval statement, so it means that your field (which I assume is not the "<fieldname>" but the name of a field) is not in that format.
| makeresults | eval x="2023-02-02 04:02:01" | eval date=strftime(strptime(x,"%Y-%m-%d %H:%M:%S"), "%m-%d-%Y %H:%M:%S")
| loadjob savedsearch="nobody:splunk_fcr_evo:last_31_days_monitoring_data"
| eval New_date=strftime(strptime(Date,"%Y-%m-%d %H:%M:%S"), "%m-%d-%Y %H:%M:%S")
| fields Date, adt, FLOW, NB1, New_date
Above gives blank results in the New_date column
your Date is not in the same format as you are using on strptime. You haven’t have hours, minutes and seconds on it. For that reason this didn’t work. Just drop those away from format or use field which contains also those.