I haven't used a teleconverter on that lens, but I used to own that lens and a D3300. Based on my usage of the 55-300, I wouldn't attempt using a TC. You'd be losing two full stops of light with a lens that's already a bit on the slow side. You may (or may not) have problems with autofocus working at those reduced light levels, if the TC is even compatible (allows AF to work in the first place).
I'd suggest a purpose built lens. Sigma and Tamron both make decent 150-600mm zoom lenses. They cost $900-1300. Not cheap, but a much better option. Plus on a crop sensor camera like the D3200 your field of view will be more like 900mm on the long end. More reach!
Again, just my opinion. Some of the more experienced folks on here might be able to give
You better advice.
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