Question:

My sailmaker is suggesting I could use a code 0 (zero) sail in non-flying sail events but I thought Code 0's are considered flying sails and would therefore not be allowed in NFS events. 

Answer: (NEW AS OF 2013 RRS 50.4 Headsails - definition)

For the purposes of rules 50 and 54 and Appendix G, the difference between a headsail and a spinnaker is that the width of a headsail,
measured between the midpoints of its luff and leech, is less than 75% of the length of its foot.

A sail tacked down behind the foremost mast is not a headsail.