WASHINGTON—Mike Flynn has provided “substantial assistance” to the special counsel investigation into Russian election interference and other matters, federal prosecutors said Tuesday, recommending no jail time for the former top Trump aide who was one of the first of the president’s associates to be ensnared in the probe.

In a sentencing memo filed Tuesday as a result of Mr. Flynn’s guilty plea late last year to a count of lying to the FBI, special counsel Robert Mueller’s team recommended leniency for the former U.S. Army...