A picture of your seedlings would help a lot here. Also, what size is the pot? The stems will strengthen as they mature, and a little wind and rain will help with that.
Sort of depends upon what the eventual size of the plants will be, Jane. If they are a tall type of zinnia, they need full sun and a lot of room, so 3in. apart will be way too close together as they get big and start blooming. You may need to pinch the terminal growing tips to make them branch so they won't get too tall and floppy.
A compact growing zinnia might do fine, but you'd be wise to give them some little sticks to support them until the stems get stronger.
