Tumblr specifically states they don't allow affiliate advertising. Though I think this rule is pretty selective:
- No adult affiliates ever.
- No blatant affiliate advertising.
- They don't mind the occasional link as long as it's contextual and inside rich content.
- Don't have every post advertise something.
Granted if you're small enough you can fly under the radar for a good while, but likely you'll eventually get caught and have to start over.