No, there is no special order in which games should be played. Each game can be played 3 times each day in any order you wish.
Two things to validate:
1. Make sure you are logged in BEFORE you start the game.
2. Make sure you are clicking the "Submit Score" button. If you click Restart Game it will not give you the millsbucks.
If you are clicking the "Submit Score" button and you are still not getting any millsbucks from games then you should contact General Mills because you likely have a glitch of some sort with your account.
There are two ways to contact General Mills - via their e-mail or via a form on the General Mills SIte. To e-mail them write the Attention Tech's and the issue in a subject line
Example: Attention Tech's - not receiving millsbucks for playing games
and send it to millsberry@genmills.com
There is also a feedback form that you can fill out
http://consumercontacts.generalmills.com/ConsolidatedContact.aspx?page=http://www.millsberry.com
This form will also go to the Millsberry staff. Make sure you select the proper subject area so it is directed to the correct people.