Do flowers heal?
So after taking a few days for some testing, yes, flowers do heal fully if you water them, and it only takes one day for them to heal. If you trample something and don't water it, it'll just wilt (become brown) and then die easily to another trample/plucking.
I bought some flowers (Sun Cosmos and White Cosmos) from the Garden Shop so I knew that they were brand new and untrampled. I planted them both and ran over the White Cosmos once and the Sun Cosmos twice. I watered the Sun Cosmos and did not water the White Cosmos.
The next day, the White Cosmos (unwatered) was brown, so just one more trample/plucking would have killed it even though I originally trampled it once. I watered it and left it alone. The Sun Cosmos appeared to be fine, and I was able to run over it twice again.
The third day, the White Cosmos was back to full color again. I again ran over it twice without it dying. The Sun Cosmos was able to take another two tramples as well. I was originally going to not water the White Cosmos again, but it rained, so they were both watered.
The fourth day, today, I was able to run over both the White and Sun Cosmos twice.
Based on the fact that I was able to trample each flower twice after watering rather than just once, I'm forced to conclude that flowers fully regain their HP when you water them rather than just regaining a single HP each day. Otherwise, they would've died when I trampled them twice again each day afterwards.