I got only these 2 errors when converting flat files to database tables. The dataflow seems to work for other flat files with the same layout so I don't understand where these errors could come from.
[Flat File Source [204]] Error: An error occurred while skipping data rows.
[SSIS.Pipeline] Error: SSIS Error Code DTS_E_PRIMEOUTPUTFAILED.
The PrimeOutput method on Flat File Source returned error code 0xC0202091.
The component returned a failure code when the pipeline engine called
PrimeOutput(). The meaning of the failure code is defined by the component,
but the error is fatal and the pipeline stopped executing. There may be
error messages posted before this with more information about the failure.
I had this problem when transferring tables which contained a SQL Geometry column.
For the benefit of others with this error, I had the same issue (An error occurred while skipping data rows) but it was not due to quote marks in the file, delimiters, or qualifiers. I am not skipping any header or data rows either. So it's a pretty annoying error message, which gives no insight whatsoever into the actual problem.
Anyway I was able to get it working by checking 'Retain null values from the source as null values in the data flow' in the connection manager tab of the flat file source editor.
I was able to resolve it by setting header rows skip count to zero (0).
I encouter the same error message in a SSIS project. The problem was in a connection of flat file source. Just recreating the connection worked for me.
I agree with the answer above "files were older and had some columns missing in the header" (and I upvoted this answer). I just had the same error, and after investigation it was because the external flat file had a column missing, compared to the columns expected by the flat file connection manager. In essence, the SSIS error "An error occurred while skipping data rows" should be interpreted as meaning "Check the actual columns in the flat file source match the columns defined in its connection manager".