What does it say on the stamp?
After discussing it with my friends, the best result I can come up with now is

The characters beside the stamp characters are the corresponding ones that may be the candidates. Seal script samples are also given. Unfortunately, I cannot find a 100% convincing answer, because they can hardly form a meaningful phrase.

Character 1: 聞 or 查. Either is doubtful. If it's 查, it means the craftsman treat the vertical 丨 in 木 as two separate parts, then Character 5 will quite possibly be 木.
Character 2: 男. It's very doubtful because there're too many horizontals 一 in 田. I am almost sure it can't be 甲, because adding one important stroke  into 甲 is very unreasonable.
Character 3: 天 or 引. Either is possible.
Character 4: 下 or 爪. Either is very possible. Specially, if if Character 3 is 天 and this is 下, 天下(the world, land under heaven) is meaningful.
Character 5: 木 or 大. Either is doubtful.
Character 6: 子. Well, it's the most confirmed one.

What I should clarify is that I don't mean the candidate characters are just what I am listing. There may be some more acceptable ones. This Chinese Etymology website may be a helpful tool for you.
I agree with Xu's arguments partly:

The scripts are seal characters or bronze characters.

There may be extra squiggles adding to the characters.

A Character may be separated into two (seldom larger than two) parts and written as individual two characters. In the stamp, there may be one case: 李=木+子.


But the case of the zigzag reading order 1-2-4-3-5-6 is really seldom. I personally believe it's in this order: 1-2-3-4-5-6, or less possible, 1-3-5-2-4-6.
Jens's answer, 鳳 凰 祥 雲, are not so similar to the character shapes in the stamp (notice that there's no 凰 in seal scripts; in ancient Chinese, it will use an &quot;interchangeable&quot; character 皇 instead).
EDIT
Character 5 may be also 北.