Issue 53088: Android reloads web page when selecting file
Most likely your device is running low on memory so when you open the file chooser dialog, the browser app is closed. When you close the chooser, the browser is reopened and has no choice but to reopen the page. That's how Android works. I know it's not helpful in your case, but if that's the problem you are seeing, you are unlikely to get a fix as this is core to the whole of Android.
Try and use some task managers to close all other apps and then try thus again and see if it works better and confirms memory is your issue.