If I recall correctly, Naruto and Boruto combined their Rasengans in an attack. How about if a ninja who can do the Rasengan uses a shinobi gauntlet? Can he power up his own Rasengan by using this tool?
I'm assuming you're asking if one creates a Rasengan with a Scientific Ninja Tool, can they amplify it with their own chakra?
Well, before I answer the question, let's start with the facts.
First off, as stated by Konohamaru Sarutobi, jutsu casted by the Scientific Ninja Tool is not tied to ones own chakra, and thus can easily go astray and cause mass destruction.
Secondly, the Scientific Ninja Tools are a work in progress and more variants of it continue to be invented, as shown by Ao when he utilized the chakra saber.
Third, jutsu can only synchronize when the two casters are on the same chakra level, as shown when Sasuke matched up to Naruto's chakra level during the Fourth Great Ninja War to make an Inferno Style Rasen-Shuriken.
There are actually multiple answers to your question, completely depending on the situation at hand. Minato once stated that when similar chakra signatures try to use a jutsu together, the chakra synchronizes and forms the ultimate technique. If you seal your own Rasengan into the Ninja Tool Scroll, cast it, and try to amplify it with your own chakra, this could possibly work. However, this is most likely because the same chakra are attempting the same jutsu.
Let's assume one with uncontrollable chakra started a Rasengan and sealed it into a Ninja Tool Scroll. Then an entirely different person with "calmer" chakra uses the Ninja Tool and tries to amplify this Rasengan. This most likely would not work. First of all, the chakra is not tied to him, and also isn't similar in any way, shape, or form. The Rasengan most likely wouldn't have been amplified and completely release and explode. It always depends on the situation at hand.
One would most likely be able to strengthen their Rasengan if the chakra is similar, but remember, if the chakra is different and lightly tied to the casters influence, this most likely would not work. We can only assume this based off the current facts given on Scientific Ninja Tools.
For more information on the Scientific Ninja Tool, please check out these links: