The teen testified during a preliminary hearing a year ago that Drayton threatened to kill him, chased him to a bedroom and stabbed the knife through the door during the argument.
The family has since reconciled and has been undergoing counseling, defense attorney Kristina Wildeveld told Senior Clark County District Court Judge Kathy Hardcastle on Monday.
In court, Drayton called the victim his stepson.
"I love my son and my son loves me, too," he told the judge.
The teen, now 18, and his mother were not in court when Drayton entered his plea to misdemeanor charges of attempted battery that could have caused substantial injury and battery constituting domestic violence.
Drayton had been facing felony assault and child endangerment with a weapon charges that could have gotten him up to 12 years in prison.
Outside court, the entertainer pulled his trademark clock neckwear from beneath a red T-shirt, as he and his defense attorneys said they don't expect the Las Vegas conviction to affect a pending felony speeding and driving without a license case in Mineola, N.Y.
"I'm standing here in front of the camera," Drayton said, "not behind bars."
The New York charges stem from Drayton's Jan. 9 arrest while driving to his mother's funeral on Long Island.
Wildeveld said Drayton was paying fines to resolve that case.
If Drayton violates terms of the agreement in the domestic violence case, he could face up to a year in county jail, the judge said.
Flavor Flav has been performing on tour since his induction last year with the rap group Public Enemy into the Rock & Roll Hall of Fame.
Hardcastle set an Aug. 18 court appearance to close the case if Drayton completes counseling.