button/236KK > 236236K > jc.MP(1), rejump j.2MK delay j.2MK, j.HP~HP
button/236KK > 236236K > jc.MP(1), [2]8HK/22HK
The main difference between Serenity Stream HK and Hyouko-Sen is the j.MP(1) rejump Chun can get before continuing the combo as normal. This not only gives her a smidge more damage and corner carry, but also opens up some additional routing options. This must be performed right off the ground to only get the first hit.
Given how common it is for Chun to confirm into 236KK, it's relatively easy to extend that into more damage. Unfortunately for Chun, common juggles that work into her lvl1 or lvl3 don't actually juggle into her lvl2, meaning she'll have to spend Drive to get this unless canceled directly from a normal. Alongside 236KK, it's easy to link this super after [2]8KK, although doing so will limit her follow-up options afterwards. The additional juggle point will remove the ability to use j.MP(1) for an extension. More moves before 236236K heavily limits her juggles afterwards, which at worst will only allow for the second hit of j.HP~HP to connect.