How did Flash get his strength

How did the Flash of DCEU come into its own?

The film doesn't give a lot of details about the story of how Flash came about, but there is this dialogue between Barry Allen and a member of the Justice League:

Cyborg : I heard you were struck by lightning.

Barry : So similar.

(From memory. I'm not entirely sure which member of the JL - probably cyborg from BilltheLizard's comment - is involved and can't find the exact quote on the IMDB.)

So far there is no reason not to assume that the DCEU's canonical origin is not respected. In fact, Warner posted a video to explain the origins of Flash (with abstracts from the comics and Ezra Miller). You can see it in this article.

Specifically,

He devoted his life to proving his father's innocence until Barry was struck by lightning one night in his laboratory. And lightning was born!

Bill the lizard

This was a conversation between Flash and Cyborg. If I remember correctly, it was when they were digging ... ah, to avoid spoilers, let's just say they dug a hole.

Taladris

@ BilltheLizard: you are probably right. I think the conversation continues and Cyborg gets angry because lightning is telling him that her skills are a blessing.