I hope not. Including the momentum term which is too often forgoten, it is not

E = mc2

E2 = p2c2 + m2c4

or for massive particles more simply

E = gmc2

It is only when the momentum is zero that you have E = mc2. So, there really is no such thing as "kinetic mass". It would be just another ugly bad word misnomer like "relativistic mass". For more on the "relativistic way" of doing relativity see-

http://hometown.aol.com/zcphysicsms/srmass.htm

and

http://hometown.aol.com/zcphysicsms/meeq.htm