Calling someone ‘a plank’ is not complimentary. I suppose it’s a contraction of ‘as thick as two short planks’, the derivation of which can be found here.
Brewer’s Dictionary of Phrase & Fable states, “As thick as two short planks. Very obtuse. Two short planks laid together are twice as thick as one long one.”
Siblings are wont to call each other planks in a jocular way. Some of my grandchildren have taken to imitating planks and enjoy planking all over the place. The images are rather blurred, I'm afraid. Perhaps the person taking the photos was laughing too hard!!
Kiri and Callum planking on the London Eye
Callum planks on a car
Kiri planks on a gangplank
Callum planking in wet weather gear - appropriate for washing machines!
Kiri planks on the furled sail
I think it has given rise to a new form or social interaction:-
“Do you plank here often?”
“Shall we plank?”
“I’ll plank if you will.”
“I want to plank with you forever.”
Perhaps there will be new ditties! This one, to be sung to the tune of ‘Are you lonesome tonight?’ could be a hit!
“Are you planking tonight?
Do you miss me tonight?
Are you glad that we planked so much time?
Do you sometimes recall that you once made me fall
From the wall that I planked on in slime?
Are the places we planked still attractive and fair,
Do you wish we could plank ourselves over some chairs?
Are you looking for fun, shall I be the one,
Darling, please, are you planking tonight?”
There will be variations, of course.
“Be my little chipboard and I‘ll be your nail.”
“Two by four and four by two – we’re made for each other.”
“You’re a splinter in my heart and you hurt me so.”
“He’s as false as a laminate board.”
“They’ve been floorboarded – the bank won’t make them a loan.”
“He’s fibreglass – light, smart, hasn’t got the values of the old hearts of oak.”

You can plank anywhere!
I don’t think I’ll go planking!