You can play it as a game, but it can have real valuable results.
Create a list of ideas similar to what I create daily here. Send them to a group of participating friends. They each pick one they like to “work on” and they try to add to it their ideas and change it for the better. When they finish, they put it back in the pool of ideas so others can again take them and further work on them as well. The game ends when no one is willing or can do further work on any of the ideas in the pool.
Brainstorming is mostly seen as a group activity. Doing it alone is also very productive, often times more so. This will enable the best of both.
An app that everyone in the group uses. Each member has a given amount of time as decided in advance to brainstorm alone, writing and sketching his ideas in the app, each one as a separate “card”. When the time is up, all the members see all the cards. They go through them, and either vote on wich ones they like (probably on the last round), or just get new ideas from them. Then another round of private brainstorming follows. Do it until you all decide it’s enough.