Northern Lights in June

Your chances of seeing the northern lights in June is effectively zero. It's simply not going to get dark enough long enough (if at all) to coincide with a solar storm, not to mention the other atmospheric conditions that need to coallesce simultaneously to give you even a faint chance of seeing them. It's like going to the Alps in August and expecting to ski (well... except of Zermatt....), or going to southern Spain in January to swim in the water. Right location, wrong time of year.

For comparison, even when I stayed for within the aurora belt in Alaska over a month's time in the winter, I saw the northern lights exactly three times. For every one successful attempt, I had maybe two or three unsuccessful tries, even on nights with a high aurora forecast.

I was there in June/July a couple of summers ago and, although the aurora was in full swing, you simply couldn't see it because it never got dark enough. It was so strong that people in England could see it but we couldn't!!

If you can travel in the winter months Hurtigruten are so confident you'll see the northern lights on their trips that if you don't, they'll take you back the following winter for free!

https://www.hurtigruten.com/inspiration/experiences/northern-lights/

Looks a bit chilly, mind! But a fabulous way to see Norway.

Ian

Not a lot of astronomical twilight at the end of June:
https://www.timeanddate.com/sun/sweden/kiruna

To Edgar's point. The sun being out will obviously prevent you from seeing it but even if the sun does set in June there is a constant "blue hour" so the sky never gets truly dark ; astronomical twilight is the technical name for dark.
Nautical and Civil are the periods of light before sunrise and after sunset when there is still some light (often referred to as the blue hour or hours)
So no, you won't see it in June.