The standard error(s) of the Kappa coefficient were obtained by Fleiss (1969). Different standard errors are required depending on whether the null hypothesis is that κ = 0, or is equal to some specified value.
We give below the appropriate standard error of the Kappa coefficient for testing whether Kappa = 0:
Algebraically speaking 
SE (0) (κ) 
= 
√ 

1 
[p_{e}^{2} + p_{e} − ΣR_{i}C_{i}(R_{i} + C_{i})/N^{3}] 

(1 − p_{e})^{2}N

where:
 p_{e} is the expected proportion that agree,
 R_{i} and C_{i} are the row and column totals for the contingency table,
 N is the number of observations.

Standard errors for where the null is not equal to zero, and for the weighted kappa coefficient can be found in Fleiss (1981)