The tour companies that lead hikes to active lava flows from the Kalapana side all have agreements with the landowners.
Sometimes, the active flows are accessible by hikers from the Park side. But you will have to check with the Park after you get here about whether or not you can actually get to the lava flow at that time - it changes constantly. From the Park website:
"Surface flowing lava is at times accessible from the end of Chain of Craters Road. When it is, and if you plan to hike out to it, you should be prepared for an extremely arduous, advanced and challenging hike that should only be attempted by the most physically fit people. It is roughly 10 miles round trip from the end of Chain of Craters Road, with an estimated time to complete of at least 5.5 hours. Hiking across lava fields requires continous awareness and concentration. The lava is uneven, jagged and very sharp."
I can attest that this hike is NOT for casual or lightweight hikers. 5.5 hours is also a very optimistic estimate of the time it takes. My brother and I, who are both athletes, started out at the end of Chain of Craters road at about 6 p.m. one evening. There's no trail, even during the day, so finding your pathway at night is really tough. The park puts up battery-operated light on columns every 1/4 mile or so to show you the way, but if one burns out and you can't see the next one, you are out of luck and have to guess at the direction until you see another one. We didn't make it back out until almost 5 a.m. - 11 hours.
But even if you don't get to get close-up and personal, the park is utterly awe-inspiring, just amazing. And seeing Halema'uma'u crater at night, with the way it's acting now, all the flare-ups and activity, is brilliant.