Journal requires permission to acknowledge people: person not replying

I would submit the paper to get the process started, but send a note to the editor that Prof. X has not yet given permission to be named, though you have tried to contact him. The editor will make a decision. Perhaps the paper will be returned to you. Perhaps the decision to publish will be deferred, but review begun. Perhaps the editor will ask the person if they will permit. There are a lot of possibilities.

But in April 2020 the world of academia is in chaos due to a worldwide pandemic. Lots of things that used to take a while, now take a very long time. And some people are dealing with illness, their own or that of family members. Don't expect communication to be quick at the present time.

You could also explain this to the professor yourself, that you have submitted, provisionally, but will respect his decision. You can always modify the ack later if needed. The review process will take plenty of time.

Logically, I think the wording from the journal, "obtain permission to acknowledge from all those mentioned" means that a non-response is a lack of permission. And even with all that's going on, two emails over 10 days seems to me to be a reasonable, good-faith attempt to gain permission.

Since this relates to a software toolkit, however, the solution seems fairly straight-forward to me. Simply acknowledge the toolkit directly, and/or "the creator of the toolkit".

Or better yet, cite it as software used, if your field uses those sorts of citations.

Is this impending submission only the first stage in a long process that will include, for example, peer review? If so, there is no need to have secured the professor's permission at this point; it's just necessary that it be done sufficiently before publication, whenever that may be. And then, in the unlikely event you fail to get permission, you can strike that acknowledgement from the paper prior to publishing.

There is no need to hold up the submission while awaiting that permission.

Separate from that, if you have a contact in your circle who is a respected colleague of that professor, you could use that person as an intermediary to contact and obtain a rapid response from that professor. But it's not worth calling in favors to do that.