The phrase "a kind of complex" is correct and usable in written English.
It can be used to describe something that has characteristics of a complex or is similar to a complex in nature.
Example: "Her feelings about the situation were a kind of complex that she struggled to understand."
Alternatives: "a type of complex" or "a sort of complex".
For those rooting against Aaron, his chase produced, at best, a kind of complex ambivalence and, at worst, virulent hatred.
This quirky band excel at a kind of complex, euphoric jauntiness, best captured on Chutes Too Narrow, their most immediate work.
The human brain, too, is a kind of complex ecosystem, coördinated by messenger molecules of its own: neurotransmitters, which govern everything from the simple mechanism of pupils dilating in dim light to the unfathomable complexity of consciousness.
The Church of the Nativity, first built by the Byzantines in the fourth century, is now a kind of complex shared, sometimes uneasily, by clerics of a number of branches.
He adds that "by writing about conflict and war and mortality from different viewpoints, from different genres, in a kind of complex overlapping Venn diagram-type way, thoughts and ideas about these themes can be generated – semi-randomly!
Asphalt concrete (AC) is a kind of complex multi-phase engineering material.
This is a terrible way to formulate any kind of complex strategy – George Bush made decisions the same way.
Ms. Goldin seems to use the term as shorthand for a kind of Pygmalion complex.
"I interviewed a lot of collaborators, and they have a kind of inferiority complex," Mr. Cohen explained.
What do you feel you achieve when you enter into a fictional world?I used to say that it was a kind of power complex.
For many Africans, the whole ideology that the western world was more sophisticated became internalised into a kind of inferiority complex.
