Can a 14 year old take alka seltzer plus?

No.

Alkaseltzer contains aspirin which we generally do not give to children for fear of Reye Syndrome ( a severe neurologic syndrome that happenes when you give kids with certain viral infections aspirin).

If the child is having headaches a better choice would be Tylenol or Motrin.

If the child is having upset stomach a better choice would be Maalox.