www.alphadictionary.com

I will leave it to the reader to judge the relevance to any current events of the definition of this term.

https://en.oxforddictionaries.com/definition/trumpery

NOUN
1. Attractive articles of little value or use.
‘None of your woollen drapery, nor linen drapery, nor any of your frippery or trumpery. I hate ostentation’

1.1 Practices or beliefs that are superficially or visually appealing but have little real value or worth.
‘he exposed their ideals as trumpery’

ADJECTIVE
archaic
1. Showy but worthless.
1.1 Delusive or shallow.

Online Etym Dict traces to triumph, from victory through a card game called Triumph. Trumpery comes from trump, which means beat or whip, thus the strong cards that trump others. Trumpery has slid toward reversing its meaning...

Not sure about that. Trump is also from tromper, to cheat or deceive, something to do with blowing a trumpet to bring the marks over before making off with their cash. It's pretty much perfect.

That is perhaps why trump is also used for flatulation at least in the UK.

It's beginning to find a similar use here.

...trump is also used for flatulation at least in the UK.

I like this one. Wonderful connection to hot, rancid air. How is it used? Or would a sample be offensive?

Depends how easily offended you are, but it's roughly as offensive as 'drop one' or 'blow off' and would be used similarly. "Watch Grandpa doesn't drop off after lunch, he's liable to trump after eating beans."