I expect you'll have better end results trying to resolve your issues with SSIS/MySQL than using a linked server to bulk insert.

If you really must use the linked server for the insert, you'll need to generate the full insert statement from your data.

Declare @sql nvarchar(max) = N'';

SELECT @sql = @sql + N'INSERT INTO MyRemoteTable (ColA,ColB,ColC,ColD),VALUES(' + col1 + N',' + col2 + N',' + col3 + N',' + col4 + N');'

From MyLocalTable;

The dynamic SQL must be runnable on your MySQL database. Once you have that built out, you can Execute the @sql across the linked server. Linked servers are most useful for small volumes of data. Depending on the number of records, you may need to chunk it to prevent sending a massive insert statement across the wire in one go.