analyse the reasons of Flimnap's enmity with Gulliver.

From the text:

"This lord, in conjunction with Flimnap the high-treasurer, whose enmity against you is notorious on account of his lady."

Flimnap's enmity of Gulliver is caused by the rumors that Gulliver is having an affair with his wife. This of course is ridiculous and impossible, as the woman is maybe six inches tall.