when people start to lash out
and act out of character, or make big scenes and blow outs due to jealousy, those tantrums are more just the symptoms. She is obviously not upset about whatever "issue" she blows out of proportion, however she definitely has a hard time speaking about her jealousy.
Because you recognize this -- if you approach can approach the friend gently enough -- in however the right manner is that will get this friend to hear the truth that you are her friend, that you do care, and that it is OK to talk about what is bothering her.
Sometimes it doesn't matter what you say or do, the friend will refuses to listen and continue to believe she is getting as upset as she does because the clothes were still a little damp when you took them out of the dryer.
But sometimes people will understand and there is hugs, good tears, and apologies. Other than that it's all the standards that I am sure you have heard before, honesty, openess, communication, respect, etc... but practicing honesty really goes a long way because believe or nor, close friends can tell when you are lying. People really are that intuitive, they just don't know it