Yes, it is possible to use estout with mfx; I just did so the other day.
Here is a fragment of the code that combines regression results (from
ivreg2) with mfx results by use of the eret2 command (part of estout).
The estout call can then refer to stat(eta etase).
. ivreg2 v_`p' (uncert = `ivlist') infl LIBOR3mo indus*, ///
> gmm kernel(par) bw(4) robust
78. local keeplist uncert infl LIBOR3mo
79. est store col`np', title(`ti')
80. mfx compute, eyex
81. mat nu = e(Xmfx_eyex)
82. local eta = nu[1,1]
83. mat nuse = e(Xmfx_se_eyex)
84. local etase = nuse[1,1]
85. est restore col`np'
86. eret2 scalar eta = `eta', replace
87. eret2 scalar etase = `etase', replace
