Is the flèche still used in foil and épée at a high level, or is it outdated?

Yes, the flèche is still legal and still used in foil and épée at the top level, but as a situational weapon rather than a main attack. A flèche is a running attack: you extend, launch off the front leg and let the back leg cross past the front, aiming to land the touch before your back foot comes down. Sabre is the exception. It bans the flèche and any forward step where the rear foot passes the front, which is why sabre fencers hop and use the flying lunge instead.

In foil it is mostly a surprise finish. Strong foilists use it to chase an opponent retreating out of lunge distance, to break the rhythm of a long exchange, or to riposte from slightly too far for a lunge. Many now use a hybrid, a leap off the front leg with the arm held back until late. Be careful with that: an attack is correctly made only when the arm straightens before the lunge or flèche begins, so a bent arm action can be called preparation and lose to a simple attack. A run of crossing steps forward counts as preparation too.

Épée suits the flèche well, because there is no right of way and the whole body is target. It is a classic way to finish an attack from longer distance, or to close fast after taking the blade with a beat or bind. The risk is the same in both weapons: once you commit you cannot change direction, so a well-timed parry, a sidestep or a stop hit catches you with nowhere to go. A mistimed flèche in épée often just hands your opponent a clean single touch.

A few rules keep it clean. Contact at the end of a flèche is not a fault by itself, but crashing into your opponent hard enough to jostle them counts as brutality and earns a red card. Running past is allowed: a hit they make immediately, even while turning, still counts, and any hit you make after passing does not. Running off the side with both feet to avoid a hit is a yellow card. Learn it from a coach first, slowly and in balance at a target, before trying it in bouts.