Your own linked study indicates that the increase in food stamps may have contributed as much as 3 percentage points of the 15% increase in food prices.
That doesn't sound nearly as impressive as the phrasing in the Fox News article you liked to. Try rereading the article and removing all superfluous adjectives. That's a good method regardless of source, by the way. If an article relies on adjectives to make its point instead of actual facts, that's a big red flag.
Obviously, any increase in money to "the people" contributes to inflation. That's just the way it is. Cut taxes? Yeah, that increases inflation.
The only way to cut taxes and not increase inflation is to only cut taxes for the very rich, since they tend to not increase their spending as much.