Hey just figured this out myself. Looks like the button to open the form has an option for Single-click: Button can only be clicked once and it's enabled by default (not sure why??)

If you disable this, it should (hopefully) allow everyone on the channel to submit.

Steps

1. Click the Edit button (pencil icon) on the message that's being sent to your channel (will probably be step 1 in your workflow)
2. Click the Edit button (pencil icon) on the button in the bottom 'button' section
3. Uncheck the setting for 'Single-click - Button can only be clicked once'

I'm not allowed to post pictures directly to Stackoverflow yet, so I have to add a link to the pic, but here's what it should look like.

https://i.sstatic.net/Um6ezL7E.png