Amid all of this type of behavior from her, if you are still looking to pursue an fwb relationship with her, it may work to your benefit to start with friendship.
Her insecurity may stem from the feeling that she can’t trust anyone that she dates. It may be best to work on gaining her trust through fostering a friendship with her first.
In time, if she comes to trust you, she may be more open to the idea of having an fwb relationship with you.
Try not to get drawn into a fight with her over what she is currently angry with you about. Instead, start the next conversation with her by asking her an open-ended question about herself.