The government's target is 95%, however, figures from September showed only 45% were being seen.
Children's mental health in Kent is handled by Sussex Partnership NHS Foundation Trust. In Sussex the trust has met the government target.
Clinical Director Dr Saqib Latif said services in Kent were "stretched".
Children are treated for a range of mental health problems including depression, anxiety, ADHD and autism.
Dr Latif said: "We are able to achieve the targets in Sussex, which shows it is achievable... but we are currently stretched beyond our capacity in Kent.
"The number of referrals we're receiving in Kent is much higher than expected by about 25%.
"And the number of emergency referrals in one month is equivalent to what we were expecting to receive in the whole year."
He said extra funding had been agreed to help reduce waiting times.
The Sussex trust took over from Kent and Medway Partnership Trust in 2012, because some patients in West Kent had waited 18 months for an initial assessment.
95%
of children should be seen within six weeks of referral, according to NHS guidelines
45% of children are seen in Kent within six weeks
Lucy Russell, from the charity Young Minds, said services were underfunded, adding that half of mental health problems start before a person is 16 years old.
"They are under incredible pressure and there's been a number of funding cuts and young people being referred to theses services is increasing," she said.
"Having targets like that is a good thing but it doesn't look good when those targets aren't reached."
More than half of children and teenagers in Kent with mental health problems are not seen by a specialist within six weeks of being referred.