Below are some tips that would be helpful:

• The best way to improve fluency is by practice. Speak as much as possible with your child in English. Children learn a lot by way of imitation. 
• Also, encourage your child to talk back in English even if he or she makes mistakes. When they make mistakes, you need to correct them.
• Another good way is to have them interact with good speakers of English. A daily 30 min to 1-hour conversation session would be great to start with.

Firstly, as most people think, communication skills don't mean communication in the English language alone. Communication can be done in any language effectively. To communicate well, you need to have a good understanding of what you want to communicate. That gives you a great deal of confidence to start communication. If you were referring to improving your communication skills in English, it depends on how comfortable you already are in English. Make a self-assessment of your skills thru free online assessment tests and decide for yourself where you stand and what you need to do next.
I hope this helps.