It's been reported that Trump has ordered flags be flown at half-staff for Kirk.

[UTUSN]

3. Or:

"AI overview: While in office, Donald Trump initially refused or delayed orders for flags to be flown at half-mast on several occasions, most notably for Sen. John McCain, fallen Capitol Police officers, and the victims of the Capital Gazette newspaper shooting. After facing criticism, he ultimately relented and ordered the flags to be lowered in these instances."

"Trump expressed frustration with the timing, suggesting that Democrats were "giddy" about the lowered flags (for CARTER) .
On Inauguration Day, Speaker of the House Mike Johnson ordered the flags at the U.S. Capitol to be raised to full-staff to celebrate the event, despite Biden's order.
After Trump's inauguration, the flags were returned to half-staff to continue honoring Carter."