What is the heat radiation emissivity of vacuum?
None. Or better yet: undefined.
Emissivity happens from a matter of non-zero temperature. Vacuum is not just cold matter - vacuum is no matter.
For air as well? What is the difference?
The difference is that air is particles containing energy. They can emit this energy at a non-zero temperature. Vacuum is just a word for... nothing. The emissivity of air I do not know by heart, but might be found in proporty tables. (I can see it is mentioned with a link in the comments by @pentane. This seems to be considering water vapour and other content in the air, so this value will vary a lot according to the content of the air.)
I understand that the vacuum has reflectivity of 0, So what is the other two values are in $reflectivity+emissivity+transmission=1$
Reflectivity is zero, there is no emissivity and the transmission would therefor be $1$ (vacuum lets 100% of radiation through).
And how this can be different for Air?
Some radiation hitting the molecules of air will be reflected (sent back or redirected, but not absorbed or passing through). Reflectivity will be non-zero but very small. Emissivity has a value, as mentioned above. Everything that is not reflected or absorbed and reemitted is transmitted. The equation is equal to $1$, corresponding to 100%, since these three factors include all possibilities. They will each take up a portion of the entire radiation, which in total of course is 100%.