krupa,
It would be helpful to know what industry your application is in. Either way I am about to empty my brain

this wont take long)
The standards for flammibility differ for each major industry. So do the test methods, requirements etc.
DOT has one set for trains, another for aircraft. Some states in the US such as California have there own standards. Other standards are application dependant such as upholstery, clothing, and construction materials e.g. paints, wallboard etc. All of which may be considered "plastic" or "composite".
There are many tests that fall under the term flammability. It also includes flame retardence, smoke release, toxicity, outgassing, burn through, etc.
My "composites" career has been in transportation and the listing below is a short one standards and testing criteria touched over the years. Hopefully these will offer you a place to start. I've left out others discussed in this thread.
ASTM D2863
NES 714
ASTM E 162
ASTM E 662
ASTM E 1354
ASTM E 84
OSU
ISO 3582
FMVSS 302
DIN 4102
Good Luck
Composites and Airplanes - what was I thinking?
There are gremlins in the autoclave!