Well- when I've made puree/compote (just stewed fruit- apples, plums, blueberries, apricots, pears whatever) it's still hot, so I pop the flakes in and stir, and they sort of cook through. Same with soup, stew- I freeze a lot of stuff in small portions for my children, then if it's a bit runny after microwaving (sorry- shoot me now MN!) then I add a few flakes and let it cool to a temp they can eat it at, by which time it's cooked through in the food IYSWIM. (this applies to the fruit too- sometimes it's a bit watery after a quick defrost, so you can just put a few flakes in then whilst it cools.) I find blueberry is good as it hides the taste 
I also used to use an amaranth-based porridge (Plum baby porridge, maybe called '4 cereal porridge'?) to thicken fruit.
With normal porridge, you could just put it in at the beginning with the oats of course.
Even though my children are older than yours (I'm guessing! they are 5 and 2) I still do a lot of small portions of frozen home-cooked food because DH and I both work FT and we like the children to have a proper meal in the evening but have very little time. Also my son is very, very fussy, and actually compote/puree is about the only fruit he'll eat, so we get through a lot of that (in yoghurt, porridge, on toast (!), with ice cream
, or just on it's own).
HTH