Is it normal a engaged girl is flirting with me?

The act is not normal from her end. I suggest you to have a talk with her and explain her that as she is engaged you do not want to ruin her engagement. Have a healthy friendship with her and suggest her the same.
Best of luck.

She sounds like a skank!

Being engaged is almost like being married, so if she's flirting and expressing an interest in you now, that's sort of like cheating. Would you be interested in a woman who you know is a cheater?
Maybe she was interested in you before but was afraid to have a relationship with you for whatever reason. Now that she's engaged she feels safe enough to tell you what she really thinks of you!

Hmm, I call it cheating.. So no, it's not normal

I feel their engagement or marriage will not take long due to her behavior regardless of your involvement. I think she may fancy you for a long time, but something was preventing her to reveal her feeling before. This is a sort of psychology phenomenon. Now that she has engaged, she starts trying to relieve her inner intention.

What's wrong with innocent flirting. If she's fucking you then it's wrong.