Dan Holden, a social studies teacher at Stuart Middle School in Kentucky, set the flags alight as part of a lesson on freedom of speech last Friday, a schools spokeswoman said.
The students were asked to write an opinion paper on the flag burning, she said, adding that the burning did not appear to be politically motivated.
Nonetheless she said at least one parent had complained to authorities.
Flag burning has become a hot topic on the US political agenda, with several senior Republicans arguing that it should be banned as part of a raft of measures aimed at boosting US patriotism.
In June a proposed amendment to the US constitution allowing Congress to ban desecration of the flag was narrowly defeated in the US Senate.
Supporters of the amendment had argued that the flag was a cherished national symbol, as well as being a symbol of freedom and national unity.
Critics of the bill said such an amendment risked eroding freedom of speech and were part of an effort by conservative Republicans to paint their opponents as unpatriotic.
Holden, a teacher since 1979, has been reassigned to non-teaching duties while the incident is under investigation.