Flight engineers are required crew mambers on many of the older transport category airplanes.
A300 B models
All these planes are still flying today, and require by regulation an engineer.
After obtaining my commercial, instrument. and multi engine certification. I decided to obtain my FE ticket instead of working as an instuctor.
I had a friend at Fine airlines who told me that they offered a training course for $7,000 dollars fo the FE ticket on the DC8. After completion of the course I had the opportunity of being hired.
After the completion of my training I waited a few months before they offered me employment. However some were not as lucky and were never hired. There was really no apparent reasoning to who they hired. Some people who did very well were not offerd employment.
The best program I know of is offerd by AeroService in MIA. They offer an unafiliated program to obtain your liscence. But if you do well word of mouth will land you a job, as many of the instructors you will be working with will be pilots form carriers looking for good people.
If you do choose to go to one of these certification courses make sure the course includes IOE (initial operating experience). This will give you the opportunity to fly with an operator, and for them to get to know you. Possibly leading to a job offer.
Even if you don't make any connections you will still be eligable for employment, and would probably not have trouble landing a job if you are determined.
It's a great alternative to flight instructing. I was flying a DC8 as FO with 320TT. As an FE I was making $48 dollars an hour. I was able to support myself, and gain valuable experience that most are not exposed to until much later.