Of course 打っときます cannot be found in dictionaries because it is not a one word. As he explained it consists of some words (contraction of conjugated verb + particle + conjugated verb + polite form).
打つ + て + おく + ます
= 打って + おきます
= 打っときます
You know, it is impossible for a dictionary to cover every possible combination of various conjugated words!
~ておく (te-form verb + oku) is a useful expression, meaning "to do (something) in advance for some purpose" as
@Glenn san explained.
I cannot think of what ぶっとぶちげる(うっとぶちげる?) could mean.
ぶっ飛ぶ(ぶっとぶ) is to fly [away] or be blown (とぶ) with a prefix for emphasis (ぶっ )(which is very rough word by the way), but cannot figure out what ちげる could be.... Of course in anime and manga sometimes characters uses very strange expressions or words/phrases original to them.