For example, when someone "pinky promises" something and then when they have to do what they promised they don't want to do they come up with excuses, for example they'll say "I never said it promises a time of when I will do it". What are words to call a person like this, basically someone who doesn't keep their word, but I need other works.
I think such a person is flake
Flake: a person you can not trust to remember things or to do what they promise
In your example:
for example they'll say "I never said it promises a time of when I will do it".
They actually didn't break a promise or tell a lie, they just cheated.
So, I would call them cheater.
A person who acts dishonestly in order to gain an advantage. (Oxford)