Can I use my Schengen visa to travel from Finland to Italy?

There are several variables and several questions here:

1. Have you told about your visit to Italy on a visa application form?
2. How much time are you going to spend in each country?
3. Will you get caught if you violate conditions of your visa?

Since this is a single entry visa, it should be issued by the country which is your main destination (unless main purpose is transit). If you intend to spend, say, 5 days in Finland and 1 day in Italy, and you have disclosed that on your application, you should be OK.

If, however, you got your single-entry Finish visa just for the sake of convenience (e.g. shorter line in front of the consulate), and intend to spend 1 day in Finland and 1 week in Italy, and failed to disclose your intention on a visa form then you are in violation of Schengen visa rules.

Will you get caught? It depends. Not likely, but

1. it is possible to encounter an inter-Schengen border control.
2. upon admission to Finland border guards may become aware that you are flying to Italy a day later (e.g. by doing a baggage search).

Now that you have clarified your itinerary, you have gotten answers about the legality, so I'll just say a little about the other part of your question.

The mode of transportation doesn't matter, so yes you can go by plane. I would in fact recommend going by plane.

Last year we had a question about driving from Portugal to Finland by car (What is the quickest way to get from Portugal to Finland by car?), a lot of the problems listed there will also apply if you substitute Italy for Portugal.