You should have the employers ID number to sell at the market. This is because the number is identified as the Tax identification number and must be used to identify business entity. However, you need consult the local city council for reference.
The vast majority of flea markets allow anyone to sell. You do not have to be registered as a business with an EIN number - you can sell as an individual. I would be very surprised if you needed an EIN number. Why don't you call them and ask?