How should I flag a post which indicates a commercial purpose?
Some posts have expressions like: "for my client", "it's part of project in my job", etc.
Are posts like these compatible with the SE idea?
You don't necessarily need to flag the post at all.
Flags are largely intended for things you can not do yourself. Either input from additional members of the community is needed, or one of the, very few, moderator only actions is needed.
Stating why a question is being asked is generally not, in and of itself, relevant to the question. I would suggest that in this specific case, you can just edit out that fluff.
Now having said that, that does not mean this post couldn't use other actions that would require a flag. But for the specific sorts of text you are inquiring about, you can just remove the text from the post, and there is still a question left, that may be of interest to the community.
Side Note: The SPAM flag is different because the post: Exists only to promote a product or service, does not disclose the author's affiliation. These posts should be flagged as SPAM because the poster of SPAM is dealt with more harshly.