“How can I reduce swelling after a gum graft?”

You can reduce it slightly by applying ice from outside the mouth, as well as some ice chips to let melt in your mouth. Beyond that, I wouldn't recommend doing anything else. Your anti-inflammatory meds - Advil, Tylenol,... will help as well.

Hello~
Typically swelling is a way that your body deals with trauma. It is a
defense mechanism to allow your body to heal.
After surgery you may have swelling present for a number of days.
Right after surgery it is important to follow your dentists recommendation
with using ice.
I recommend to my patients to use frozen peas or corn packages with placing
the frozen vegetable pack on the wound site 20 minutes on and then 20
minutes off around the wound.
Just like anywhere else on or in your body, you have had surgery and it
taken time for healing.
Be kind to yourself, and follow your dentist’s instructions.
Best of luck,
~Dr. P

A cold compress or ice pack is a good way and there are medications you can
take but honestly ask your dentist about what to do for your specific
situation. Each surgery and person is so different, they would know best!