A full-thickness burn is going to cause a lot of problems; an increased risk of cancer down the road is likely to be the least of your problems.

That said, inflammation and tumors are surprisingly tightly linked: many tumors co-opt inflammatory pathways, or use them to establish favorable "micro-environments" that allow the cancer to proliferate.

Here's a review about the link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2803035/