A similar flag was behind the Grenfell model in the video.
A sixth man handed himself in to police on Tuesday.
On Tuesday, police searched a home in South London where the bonfire is believed to have been lit last weekend.
They have been taken into custody.
Campaign group Justice4Grenfell has called the video a "sickening act of hate", saying it has caused "great alarm and distress".
"I am very pleased to hear that the authorities are taking the matter very seriously and that an investigation is under way". "Any offences that have been committed will be fully investigated".
Campaigners described the video as a "sickening act of hate".
London Fire Commissioner Dany Cotton described the footage as "appalling and disturbing", adding it "cannot be justified on any level".
She said she did not know the origin of the video, but it was being shared via messaging service Whatsapp. Many of those who died in the Grenfell Tower fire were Muslim and from ethnically diverse backgrounds. "It can not be justified on any level".
Video footage of Britain's sickest bonfire showed people suggesting that the victims of the blaze - which killed 72 people a year ago - hadn't paid their rent, as one person dubbed a crude cartoon of a Muslim woman on the effigy a "ninja".
An inquiry into what happened is now taking place.
In the video horrific comments and jokes were made about the victims of the fire represented on the bonfire - angering and devastating hundreds of people on social media. As the flames consumed it, people in the group chanted "help me, help me".
"It's amusing regardless. It doesn't mean I'm not a compassionate person, it doesn't mean I don't have sympathy".
The fire, which ignited on the night of June 14, 2017, marked Britain's deadliest domestic blaze since World War II and became a symbol of the area's stark inequality.
A third person shouted: "Jump out of the window!"
Mr Elouahabi was also due to receive resettlement payments worth a further £14,730 to go towards housing and free utilities before the fraud was discovered.
At the end of the clip, someone else can be heard saying: "That's what happens when they don't pay their rent". If you can, please show your appreciation for our free content by donating whatever you think is fair to help keep TLE growing.
"We have support and will carry on with dignity until we get justice".