How long is it supposed to it take chlamydia to cause pid?

Hard to say. It is well known that stds such as chlamydia, especially in long standing infections, can lead to pid; however, pid ranges from subclinical and asymptomatic to severe, so it is impossible to give a time line because 1) many patients don't even realize they have pid and 2) the progression will depend on host immune system function. If you are concerned, you can be checked for active disease.