I did not find code to fit a skewt distribution with the gamma parametrisation.
Maybe this works for you.
library(fGarch)
#> Warning: package 'fGarch' was built under R version 4.1.2
#> Loading required package: timeDate
#> Loading required package: timeSeries
#> Loading required package: fBasics
set.seed(2021)
n <- 10000
r <- rsstd(n, mean = 0, sd = 1.1, nu = 5.2, xi = 1.3)
fit <- sstdFit(r)
fit$estimate
#> mean sd nu xi
#> -0.01468788 1.07768059 5.74581257 1.30790698
Created on 2021-12-18 by the reprex package (v2.0.1)