Flea bites are not always itchy, but the vast majority of the time they are. That is because flea bites cause any allergic reaction in the skin of most people, similar to the reaction of a mosquito bite.
When the flea extracts blood from its host, it also injects chemicals into the skin in order to anesthetize the area so that the host will not detect that it is being bitten.
There are also anticoagulant enzymes that are injected into the skin so that the blood will continue to flow and not coagulate. These are the enzymes that cause the allergic reaction which makes the flea bite becoming itchy, red, and raised on most people.
Some people have a more severe reaction to flea bites and their skin will develop a severe rash as well. Conversely, some people have hardly any allergic reaction and all and do not see any of the normal symptoms of flea bites. These people are very lucky indeed.