You can use Amazon DynamoDB without restrictions from about everywhere - a nice and helpful demonstration are the AWS Toolkits for Eclipse and Visual Studio for example, which allow you to create tables, insert and edit data, initiate table scans, and more straight from your local development environment (see the introductory post AWS Toolkits for Eclipse and Visual Studio Now Support DynamoDB).
Other than the obvious higher latency, are there any security or performance considerations when using my own server?
Not really, other than facilitating SSL via the HTTPS endpoint, if your use case requires respective security.
In case you are not using it already, you should check out AWS Identity and Access