On the first visit to the veterinarian's office, Cora's kitten weighed 550 grams. On the second visit, the kitten had gained 350 grams. On the third visit, the kitten had gained another 300 grams.

What is the percent increase since the first visit in the kitten’s weight rounded to the nearest percent?

The total weight increase since the first visit is 350 grams + 300 grams = <<350+300=650>>650 grams.

The percent increase since the first visit is (650 grams / 550 grams) * 100% = 118.18%.
Rounding to the nearest percent, the percent increase is approximately 118%. Answer: \boxed{118}.