>>For some reason the spell doesn't slow. I tried adding the "Slowed" buff instead of Breath of Frost but it also didn't work.
Hmm, you just base off 2 skill by Breath of Fire and Breath of Frost.
Add BoFire to the dragon and BoFrost as a triggered spell.
Everytime the dragon cast BoFire, wait .2 second before casting BoFrost.
(Ofcourse, make 2 different buff for BoFire and BoFrost)
>>BoFrost as a triggered spell.
Yes, based off Carrion Swarm (which has no buff) with different projectile. The trigger should create a dummy unit which casts slow with modified buff (Slowed) at units nearby of the target (point or unit [including the target itself]). I can be wrong though