For second stage its easier to use push pull topology with a center taped transformer.(because of low output power and low primary voltage)
use something like UC3525 and two irfz44 as main switches. make the cintroller to work at max duty cycle.(by connecting the noninverting to vref and inverting to the gnd)
at the secondery use 4 diodes and a cap like 22nf/1600v like a simple rectifier.
it will work.