Hi,
I would recommend you build a few AIMMS pages to show the value of variables and parameters. You can also add a button to run the solving procedure and buttons to navigate between pages. So your work flow will be click the button to run the model and see the results on the page.
You can also export AIMMS results to Excel, database or text file.
AIMMS does have API with python and matlab. But unless you need link existing code of those systems, I would not recommend taking this route.
Best,
Deanne