Literally "has little use for/of" means that someone doesn't often need to use something.
The tallest man in the world finds little use for a ladder.
Sometimes the expression might be used as an ironic understatement (litotes). Here it means "doesn't use at all"
A fish has little use for a bicycle!
The participle phrase has the same subject as the main clause. Trump is finding little use for empathy.
So here it means Trump was not using "empathy" or "truth" when he wrote his tweet. So it means that the tweet by Trump was a cruel lie.