Another of the teenagers appears to film his actions on a mobile phone.
The property in Larne Road, Lincoln was targeted overnight on Wednesday (7 February).
A Lincolnshire Police spokesman said: “We have received a report that a hosepipe was put through a vulnerable resident’s letterbox and turned on causing flooding to the property.
“We know that the faces of those on the footage cannot be clearly seen, but we believe that their mannerisms and clothing will be recognisable to those who know them.
Anyone with information can call police quoting incident number 371 of 7 February.