Got one!
Please measure the amount of time it takes these flies to do some unmentioned tasks. Also, become fond of an arrow.
Or then there is the symbolic meaning, but applied to the arrow as a shape rather than as a physical item. Time flies in such a way that it goes straight forward for a while, spreads out suddenly, and then tapers to a point.
Use your stopwatch to ascertain how quickly people can zip up their pants in a swift, straight manner.
Confucius say: When attempting to cook long, straight strips of potato (that are sharply tapered at one end) in oil, it is necessary to time the operation precisery.
Find some flies that are similar to an arrow, and time them.
That is equivalent to the third one in the OP.
Yea, I realized that after I posted it, but too late to edit it.
She bears each cross patiently?
Would you care to explain?
If you fold up this news magazine (the world's largest) just so, you can project it through the air a considerable distance, and with considerable accuracy.Just another phrase with many possible meanings.
Darn, the last has been done and I missed the edit window. 
Oh, I am with you now: like the striptease artist distracting drivers and making things difficult for pedestrians.
Has this one been done:
The objects known as “time flies” are similar to arrows in an unspecified way.
It should really have a comma: Time flies, like an arrow.
Wait, so are we allowed to add punctuation? Because if so, it could be a Valley girl making fun of that geeky pilot named Time…
“Time flies, like, an arrow.”
Well you wouldn’t necessarily need punctuation in my example, it would just be a sentence fragment. Upon checking the OP it did specify “phrase” rather than sentence.
You could use it in a sci fi novel to describe the action of “time flies”:
The time flies like an arrow did plunge into the center of the combat.
A Pierce Arrow was an automobile and as such didn’t fly at all. So if time was passing slowly, you could sarcasticly say that time is flying like a car.
The amount of force exerted by the passage (or flight) of time is approximately that which would be represented by an attonewton using arrow notation.
The time that flies like is an arrow. (This would not be correct grammar except in newspaper headlines, but still, constructions such as this are used regularly. Or should I say “Constructions like this used regularly”)
Both sem and gram. The phrase was coined by someone or other in early work on AI precisely to play with a computer’s “understanding.”
Time I left
Time for bed
Time flies like an arrow