There is not a legal third presidential term for President Trump or any other former Presidents of the United States. While I could not access the specific article that talked about the alleged legal loopholes for this because of a paywall, I looked at commonly used points Trump supports claim. Their main argument for this is that while he couldn't be elected for a third time, he could run as a vice president, then the president could relinquish power and he could become president due to succession.
Section one of the 22nd amendment outlines the following as this,
"No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once."
While there is no specific verbiage against what these people claim, the language of the constitutional amendment is very clear in the message of no one being able to hold office for more than two years of a term, even if someone else was originally elected.
Furthermore, in the BBC article Legal experts stated this
"... said the Constitution's 12th Amendment says
'no person constitutionally ineligible to the office of president shall be eligible to that of vice-president of the United States'"
This means that there is no current way for President Trump to be legally able to run or assume duties as President for a third term.
https://www.bbc.com/news/articles/cx20lwedn23o
https://constitution.congress.gov/constitution/amendment-22/#:~:text=No%20person%20shall%20be%20elected,the%20President%20more%20than%20once.
