How many hours in between do I need to safely take fluoxetine and use diclofenac suppository (100)?

Hi, Parrr!
The half life of fluoxetine is several days so there will always be some in your system. All you can do is separate your doses as much as possible.
This type of interaction is fairly rare and your doctor should be aware of the possible interaction. They have probably determined that the benefits of the two drugs outweighs any potential risk to you.
You should address your concern with your doctor but it's not very likely that you'll have a problem. Just be alert to any unusual bruising or bleeding.
Best regards, Wildcat
Good for you for doing your research!