Can I claim a tax credit for my 23-year-old kid who claimed himself on his taxes and selected the box “no one else can claim him as a dependent” for 2017?

Your tax return will reject if yo try to e-file it.  You can file if he made a mistake and you are eligible to claim him, but you will have to file on paper in the mail.   He can file an amended return to change his answer to that question, but it takes the  IRS 3 or 4 months to process an amended return, so you will need to file on paper this year if you want to claim him.