Give a word for momentarily touching something repeatedly

You're looking for the word 'tap'.

This is how the Cambridge dictionary defines it:

Tap: To hit something gently, and often repeatedly, especially making short, sharp noises.

Example: The branches tapped against the window.

the branch "flapped" against/on the wire?

A possibility is click:

[Merriam-Webster]
1 : to strike, move, or produce with a click
// clicked his heels together

Using the present participle conveys the sense of repetition:

She heard the tree branches clicking against the electrical wire.

Trees sway in the wind, and when near electrical lines, they can beat those lines like waves beat the shore. From M-W:

sway: the action or an instance of swaying or of being swayed : an oscillating, fluctuating, or sweeping motion

beat: to strike directly against forcefully and repeatedly

The oscillatory motion of a swaying tree could cause it to beat a nearby electrical line, i.e., to strike directly against it forcefully and repeatedly.

Brushing is the word.

Due to the wind the tree's branch kept Brushing against the power line. The consequences could be easily anticipated and much dreaded. I find no dictionary definition takes into consideration the physical conditions involved since the conditions do not change during the storm until the disaster.

The repeated Brushing of the branch on the power line is what causes the eventual problem.