A: I don't feel well enough to go to the station to meet him.
B: I will meet him for you. Tell me how I can recognize him.
A: He will be wearing a black and white school cap.
You are correct that 'will meet' should be used for B. 'Will meet' uses the simple future tense, which is the tense used to discuss an activity that begins and ends at a point of time in the future.
'Will be wearing' uses the future continuous tense, which is used when discussing an activity that starts in the future and will continue to occur for a period of time after that.
The last sentence could be replaced with:
He is going to be wearing a black and white school cap.
'Going to be wearing' is more likely to be used if 'he' has deliberately planned in advance to wear a black and white school cap, e.g. just so that he can be spotted in a crowd.
If A is simply predicting what 'he' would wear based on past evidence (e.g. that was what he usually wears), then either 'will be wearing' or 'is going to be wearing' are acceptable.