The magnifying power does matter. It's actually stands for the focal distance parameter of a particular lens. So, the higher the magnification - the shorter the focus distance.
The shorter focus means two things for our consideration: 1. It makes the image of the sun smaller, so the solar power will be concentrated on a smaller spot, producing higher temperature compared to a longer focus lens. 2. The lens with shorter focus must be placed closer to the tinder. So if that's a plastic Fresnel lens it's easy to damage it with the heat.
Also the cheap short focus lenses (magnifying glass kind) are usually have a lot of aberrations (spherical, astigmatism, chromatism, etc), which may reduce the fire-starting effectiveness, simply diffusing the sunlight. So, I'd recommend to go for something not more than 5x power lenses (2 inch focus minimum).