As Barack Obama delivered the commutation to Chelsea Manning's 35 year sentence down to 7, would President-elect Donald Trump have the ability to reverse that when he becomes President?
The power of a Presidential Pardon comes from the Constitution (Article II, Section 2) and there is no provision for undoing it.
No, the commutation has been entered so that is set. However he did not pardon the Private, he just commuted the sentence.
Manning was convicted under the Uniform Code of Military Justice in a general Courts Martial, not in the Federal Court of law. Double jeopardy and the protection of the 5th amendment prohibition of such, does not apply here, with regards to the Federal Criminal courts. So in theory the DoJ could pursue federal criminal charges which may include espionage, treason, and many other serious charges.
While this is possible, I do not think it will happen, unless Manning decides to go out and make a spectacle of herself. This is likely a case where the government will be happy to allow Manning to drop out of the public limelight rather than keep the whole affair under a spotlight.