Development Software

You need a database that doesn't need to be "installed" for the USB flash drive. For that I recommend sqlite. You could also try XAMPP to use MySQL.

As far as phones go, you're going to need to come up with a platform-specific solution since their OSes are different (Android, Windows Mobile, iPhone OSX, etc)

There are some other options also, depending on your requirements. For example, if your database needs aren't all that complex, you might be able to run one of the flat-file based databases. There are also models in Java that might be able to run, but of course, you would have to have Java installed on your flash drive. Not all phones will be able to run java applets either, so I would first try and come up with a list of must-haves and then someone here might be able to point you in a better direction.

Sorry to be so vague, but there are many database options out there, and not all (read:most) of them are designed to be cross-platform or portable.

Besides the aforementioned options (I love XAMPP btw, I have found it to be great even in production environments), you might want to consider taking a look at http://www.freebyte.com/programming/database/#opensourcedatabases (Hopefully providing this link doesn't violate forum rules. I have absolutely nothing to do with freebyte so I won't be hurt at all if the link gets edited out. - just trying to provide some info.) That should get you started with some of your options.