I think it doesn’t work as wakeup against meaty because flamekick is actually kara cancelling the punches if you’re out of throw range. So if you do it on wakeup, you won’t be invincible until a few frames after.
I think the flame kick/chicken wing thing wouldn’t work either. For auto correct, if you’re being crossed up from right to left, the input for a flame kick would be L, D, DR + K, while the input for a chicken wing would be L, D, DL, UL + K. So the final joystick position of flame kick and chicken wing are at opposite ends. I think even if you did somehow combine the motion, you’d just get whatever was input at the correct wakeup reversal timing, nothing would auto mixup because you can’t kara cancel a special.
If you want a throw/chicken wing option select, you could do DB, D, DF, F + forward, UF + roundhouse, I am pretty sure. A rekka throw option select would be D, DF, F + Kick throw ~ punch.