Can the use of transmission fluid on human hair be dangerous?

Yes it can, though how dangerous depends on the formulation of the specific transmisison fluid. Generally speaking, automotive lubricants don't do well in contact with human bodies. Read the warning label on the back of the fluid can for details. In the mean time, get some shampoo and wash it out completely. Be careful not to get any in your eyes. If shampoo doesn't do it, try Dawn dish washing liquid (Dawn is really good at forming suds in an oily environment).