I am slipp'ry, I can slide;
Burn you with a simple lie;
Burn you 'cause I'm feeling high.
See my sister boil and blister;
She can burn you, make you flow;
Burn you 'cause she's feeling low.
Basically...
...you’re a base!
I am slipp'ry I can slide;
Soap is a base, I believe, and it’s slippery.
Burn you with a simple lie;
A reference to lye, a substance with a pH of 13, according to Google.
Burn you 'cause I'm feeling high.
Bases trend toward high pH measurements. Substances at the extremes can be harmful to exposed skin.
See my sister boil and blister;
Your sister happens to be an acid.
She can burn you, make you flow;
Strong acids can cause burns.
Burn you 'cause she's feeling low
Acids rank low on the pH scale. Lower numbers indicate greater acidity.
Are you
Coldness, or warmness?
I am slipp'ry I can slide;
Ice?
Burn you with a simple lie;
Freezer burnt.
Burn you 'cause I'm feeling high.
I am not sure becuase the temperature would be low, but it might be a trick. But maybe snow?
See my sister boil and blister;
Heat.
She can burn you, make you flow;
When you get a burn.
Burn you 'cause she's feeling low.
Again, maybe a trick, but maybe fire.
Could you be
The Sun $\&$ Moon?
I am slipp'ry I can slide;
Burn you with a simple lie;
Burn you 'cause I'm feeling high.
This paragraph talks about the moon.
It slides in the sky and looks like ice from it's white colour (hence slipp'ry). It can burn you with a simple lie: it is daytime and you might get sunburnt (the moon often appears at night). Lastly, humans have to thank the stars for our existence, and they only twinkle (or burn) at night with the moon; it is the only time where we can see them clearly.
See my sister boil and blister.
She can burn you, make you flow.
Burn you 'cause she's feeling low.
This pargraph talks about the sun.
It boils and blisters because it is literally a giant ball of plasma. You can get sunburnt and perhaps need to go for a swim (hence make you flow). Lastly, you can appear to look burnt under a red sky (because you would look red from light; you would look burnt, perhaps), which only happens during a sunset (when the sun is low in the sky).
Title:
It Runs in the Family
The family might be the Solar System (a family of planets) where the sun and the moon are. The moon runs (orbits) around the Earth, and the sun runs around the centre of the galaxy.