I have achilles tendonitis, should i wear high heels or flat shoes?

You may have less: Pain in the high heels as the achilles functions less. Ideally, you should wear neither. Stick with a good shoe or sneaker, consider a small heel lift, ice the achilles....

What is Cause?: I agree with recommendation for heel lift as it takes tension off the achilles. Question is how did it start? If gradual over time then ice, lift, stretching and eccentric strengthening-physical therapy may help. If you are limping a walking boot may help until pain calms down then progress. If this is the result of an impact injury this could be stress injury. All heel pain is not the same.