I would like to use dropbox syncing mechanism to my app, to upload images from my app.

Just to make sure I understand, you want users to be able to upload images from their SD cards to their Dropbox accounts, using the API? This is definitely possible with the Android SDK. You'll want to follow along on the tutorial here (v1: https://www.dropbox.com/developers-v1/core/start/android; though, I strongly recommend using v2, tutorial here: https://github.com/dropbox/dropbox-sdk-java/tree/master/examples/android) to guide the users through the flow to link their own Dropbox accounts, and then upload images via the API. I imagine you can make your app work in the background using Android features. 

If, however, you mean that you want users to upload all their images to your Dropbox account, that's different. The API was designed with the intention that each user would link their own Dropbox account, in order to interact with their own files. However, it is technically possible to connect to just one account. The SDKs don't offer explicit support for it and we don't recommend doing so, for various technical and security reasons.

However if you did want to go this route, instead of kicking off the authorization flow, you would manually use an existing access token for your account and app. (Just be careful not to revoke it, e.g. via https://www.dropbox.com/account/security .)