Recently, pardoned felon Michael Flynn called for President Trump to invalidate the certified democratically run election results, declare martial law, suspend the constitution, and re-run the elections under new rules that would favor Trump.

Is that possible?  According to a Wiki article on U.S. Martial Law, national-level martial law can theoretically be declared by either the president or Congress (at the state level, governors can declare it), but the Constitution is murky in this regard.  That sounds ominous, but the Posse Comitatus Act of 1878 forbids U.S. Military involvement in domestic law enforcement without congressional approval.  Basis for martial law is in Article 1, Section 9 of the Constitution: "The Privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it."  Habeas corpus is a fundamental right in the Constitution that protects against unlawful and indefinite imprisonment. 

According to an excellent and comprehensive article from the Brennan Center for Justice, “the Supreme Court has never directly held that the federal government has the power to impose martial law.”  The most recent relevant precedent is Youngstown v Sawyer (1952), in which then-president Harry Truman sought to seize U.S. steel mills to prevent labor disputes from disrupting steel supplies for the war effort. The court established that the president may not take executive action in opposition to Congress unless Congress has overstepped its own powers.

Finally, it is critical to note that declaration of martial law in no way “suspends the constitution.”  Such an assertion by Flynn shows a profound misunderstanding of basic civics, in addition to being a deeply shameful—and seditious—incitement to overthrow a duly elected government, and Flynn should be court-martialed for this.  All constitutional rights, except for habeas corpus, are completely intact, as is judicial review over presidential action.  That said, enough ambiguity exists, including when the use of military (under the Insurrection Act) is permissible, for Congress to pass legislation limiting presidential power for the future.