Two suggested answers for Rashi's question on Shemot 14:7

Yes, the title is a misnomer. The question was originally asked by the Mechilta on the verse.

And that question is as follows:

""And he took six hundred choice chariots" (14:7): Whence came the horses required for the chariots? If you would say, from Egypt, is it not written (Ibid. 9:6) "and all the cattle of Egypt died"? And if you would say, from Pharaoh, is it not written (Ibid. 3) "Behold, the hand of the Lord is in your cattle in the field, in the horses, etc."? And if you say, from Israel, is it not written (Ibid. 10:26) "And our cattle, too, will go with us; not a hoof will remain"? Whence, then, did they come?"

Now, the Mechilta goes on to explain that the horses belonged to those Egyptians who feared Hashem and listened to Moshe's warnings during the plagues that killed the domesticated animals.

But earlier this evening I thought of two other possibilities:

1. The midrash in Shemot Rabbah 10:2 says (loose translation):

"The children of Cush and the children of the Egyptians disputed amongst themselves: The Egyptians said that our border is until here and the Cushites said that our border is until here, until the frogs came, and they made peace, for it was said that the frogs would only roam through the borders of Egypt, thus they knew where the borders were."

That's one possibility - having made peace with the Cushites, perhaps they established some kind of agreement that allowed for them to borrow war horses.

2. Something that I think is likelier:

From archeological discoveries from the last century and a half or so, we know that the very best Egyptian chariot-drivers were Canaanites, called "Maryannu" in official Egyptian documents. Similarly, we find in Tanach that the Canaanite chariots were a force to be reckoned with (Yehoshua 11, Shoftim 4). Never mind now when exactly the Exodus was, it is highly likely that the Egyptians still controlled the areas of Canaan in which the Maryannu trained during the time of the plagues and the Exodus. So when the locally-stationed war horses were "decommissioned", they simply ordered the Canaanites to send them more. And these are the six hundred chariots, as well as the "bachur", which Rashi explains means "elite [charioteers]" - Egyptian-serving Canaanite Maryannu. Or else actual Egyptians, but with Maryannu equipment.

("Most esteemed Pharaoh, didn't this God just crumple you up like a wad o' papyrus with a buncha plagues?"

"Shut up and drive!"

"Yessir, only sayin' sir. So, make a left at Pi-Hachirot?"

Image taken from here)