So your question is actually:
"How do I write a MySQL client program that will run on a TS7260 or ARM9 embedded Linux system?"
1. Pick a language (Perl and Java are two excellent choices - there are many others)
2. Build the MySQL client runtime and/or MySQL server for your target
3. Write a simple "hello world" client program (to verify connectivity)
4. Write your application
In other words, there is effectively NO difference between writing a MySQL client for your embedded Linux system, and writing a MySQL client for a standard desktop Linux.
Here are some good tutorials - pick one and try it on your desktop. There should be little/no difference when it's time to migrate your work to your target host: