I would load the file into a staging table with indexing fields for filename and row#

You know that a record starts with NAME and the underscore, so find each row# that has just 'NAME' with '======' in the following row.

You now know the starting and ending rows for each record and can parse the lines as necessary.

Alternatively, In your SSIS replace 'NAME [/r/n]====[/r/n]' with '<RECORD><NAME>' replace '[/r/n]Address[/r/n]=======</r/n]' with '</NAME><ADDRESS>' and repeat the replace process for each heading so that you convert the file to a valid XML format. This will be much easier to work with as it turns it into properly structured data. Don't forget to end the record with </RECORD>