Thrush is actually pretty easy to kill. Getting to it can be a bigger problems. If it's in an easily accessable area vinegar do the job really well. It's an old way of treating it that I learned from some very old (now dead) horsemen and it's worked on my horses for over 40 years. I use a 2 parts vinegar to 1 part water mix in a spray bottle. If it's just round the surface or upper areas of the frog and open the pocket (usually completely removing the covering tissue if it's near the surface), clean if out and rinse it well with vinegar mix. I clean and rinse it daily for about a week (I'm known for doing overkill with thrush). In cases where it's deeper in the frog (I've had new horses come with it down in a crevasse) clean is best you can (I'll use cotton or gauze to push down inside with the vinegar mix to "swab" it out as much as possible) rinse well with the vinegar. I then pour tea tree oil into the area and pack it with clean cotton or gauze soaked with tea tree oil and leave it. I will actually be ok to leave it for a week to 10 days, but I usually replace it after about 4 days. Rinse and repack again. The thrush is usually gone after a week, but I continue the treatment for a week longer just because I never like taking chances with thrush.
You may hear some people specifically say apple cider vinegar. ACV will do the job, but the only difference I've seen between using apple cider vinegar and white vinegar is that the ACV makes the foot taste better