I can say from personal experience that it is very easy to brainstorm all the time but very difficult to just do so at the right time and to do so well. I still have all kinds of issues with it, but have put together my pondering on the topic over the last couple of years in two articles and a bunch of worksheets:
Articles
Brainstorming problems and solutions
Different ways of brainstorming in EFL – LINK FIXED
Other blog posts with relevant worksheets
https://tefltastic.wordpress.com/2013/04/03/discussion-questions-for-brainstorming/
Worksheets
Phrases for brainstorming in pairs and groups presentation and practice
Needs analysis and phrases for group brainstorming presentation
Improving education brainstorming phrases practice
Brainstorming to present and practise other language
Brainstorm and rank comparing and contrasting phrases
Brainstorm useful phrases for IELTS Speaking Part Three into the gaps
Hedging/ generalising phrases brainstorm into the gaps
Brainstorming for job applications
Sharing experiences of using and learning English (useful for needs analysis and presentation of useful phrases)
Sharing experiences key words brainstorming and speaking games
Correct, simplify and brainstorm sharing experiences phrases
Brainstorming phrases for sharing personal experiences
Clarifying phrases key words brainstorming
Post-discussion discussion and brainstorming
Completing telephoning phrases brainstorming and roleplays
Brainstorming clothes and accessories game (for young learners)
Social issues brainstorming and speaking
Current affairs vocabulary brainstorming and speaking
Brainstorming language for IELTS Listening
Body parts brainstorming for prepositions of position
Business English questions brainstorming
Challenges 1 brainstorming revision game
IELTS Speaking vocabulary brainstorming
Food business ideas brainstorming meeting
Sports brainstorming and discussion
TEFLtastic 
New idea on this topic: brainstorming different topics of vocabulary to the tune of the song English Country Garden.
Haven’t tried it in class yet, but my three year old daughter quite enjoys it…
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