There is most definately work available for qualified flying instructors - just depends whether you're lucky enough to be at the right place at the right time. Failing that, you'll find work (albeit part-time work) somewhere if you are prepared to look around and contact the flying schools by telephone or in person. Show your face around prior to commencing the FIC and you'll be more likely to succeed post-FIC in securing work. Worked for me.
Good luck!
VFE.