If you have a cluster of points selected like this:
how do you align the points so that they create a flat plane?
You can achieve this by scaling the points along a perpendicular (Normal) axis:
Via Keyboard:
Normal
Via Mouse:
Then you need to left click anywhere in the scene to confirm and modify the properties of the tool.
And you will get all the points aligned.
If you scale the vertices to 0 along a specific axis, you can make them flat. For example, if you want to flatten some vertices along the X axis, you would press S (to scale) > X (for the X axis) > 0 (to scale them to zero).