What are some good, inexpensive ideas for a flower garden at school?

This is not a flower, but my kids used to grow beans in paper cups. They grow so fast and are fun for them to watch grow and easy to take home.

Chakaris...would the school approve a raised bed in a designated area?

There are often grants to be found to create a school garden but you can also create one inexpensively if you just tell the children and their families what you need. It could be simple or elaborate. Here are some examples-

Plastic egg cartons and seeds for small growth plants. Enough sections so each child has a plant to take home when you cut them apart at the end of experiment.