If you're looking for a way to make the word more intense or formal, you might consider:
* Adding "very" or "extremely" in front: "very kindly," "extremely kindly"
* Using synonyms like "graciously", "generously", "considerately": These words have similar meanings and might suit the context better.
For example, instead of "He kindly offered his seat," you could say:
* "He very kindly offered his seat"
* "He graciously offered his seat"
* "He generously offered his seat"