How can the thermal conductivity of a binary gas mixture be estimated?
I'm thinking you could use the Fourier equation for heat flux

$$
\phi =K \frac{S\theta}{e} \,\, ,
$$
where


$\phi$ = Heat flux
$K$ = Termal conductivity coeficient in units of  $kcal  s^{-1}\ m^{-2}\ K^{-1} /m^{-1}$
$S$ = Area of the section you're dealing $m^{2}$
$θ$ = Difference of temperature $K$
$e$ = Thickness in $m$.


And use for the resulting thermal conductivity the fraction

$$
K_{r}=\frac{\sum K_{i}J_{i}(M_{i})^{1/3}}{\sum J_{i}(M_{i})^{1/3}} \,\, ,
$$
where:


$K_{r}$ = Resulting termal conductivity of the moisture;
$K_{i}$ = Termal conductivity of each gas;
$j_{i}$ = Molar fraction of each gas;
$M_{i}$ = molar mass of each gas.


I think it'll work with some 2% of standard deviation. If you're able to read in portuguese, here is the link of my reference:

Reference

And here is the link of the Book cited by @Chester Miller.

I hope I hope I was Helpfull!