How much energy do we need?
Well, the escape velocity of the Earth is $11,180 m/s$. To accelerate 1 gram to this speed, you need:
$$\frac{mv^{2}}{2}$$ $$\frac{1g\times (11,180m/s)^{2}}{2} = 62.5kJ$$
To find out how we could possibly generate that kind of energy, the heat of combustion of methane is $55.5kJ/g$. It seems like this might not be as far fetched as it would seem at first glance. (Though I would suggest that your seeds are made of handwavium to explain why it survives the explosion and the air resistance it would face)
What's the evolutionary advantage of intermediate steps?
I think the first step isn't too terribly unlikely. Imagine a plant that produces seeds and then explodes when it's ready, thus spreading its seeds over a larger area. You could even say that the underground parts of the plant survives the explosion and grows back in a few years. Now imagine that this plant looks a bit like another plant that the local fauna likes to munch on. And that, when you apply too much pressure to this plant when it's ripe, it explodes. 912
This would result in most of the seeds flying off as usual. Some seeds would hit the animal though. And if these seeds have enough kinetic energy, they might even kill that animal. This ensures that the seeds have plenty of food when growing into plants themselves. As a side effect, some seeds could be shot straight up. I'm not quite sure how to justify the step from seeds flying fast enough to reliably kill an animal to them flying fast enough to escape the gravitational pull of the earth (let alone the solar system). Some wild suggestion that pop into my head are a weapon race with an animal that develops thicker and thicker skin and the idea that if you explode hard enough,you might kill some animals standing a few meters (or kilometers) away as well.
What is the benefit in the end?
I think this is where it falls flat, If you somehow manage to reach escape velocity and against all odds actually hit another planet and this planet is capable of harboring life, you still only have one plant (correction, one seed) in an ecosystem it is very likely not at all adapted to thrive in. Hardly a big advantage over other other plants.
Luckily as the writer you can just decree that two nearby planets (or a planet and its moon) just so happen to have similar ecosystems. 258