The flow has already started to show signs of reversing, in the wake of DHS's buy-ups of huge stockpiles of ammunition. Mexico has plenty of laws regarding drugs, but that hasn't abated the flow of drugs. The problem is an appetite for guns in the country bordering Mexico's northern border, but it's not an appetite that is likely to go away by making guns illegal up here, any more than us making crack and heroin illegal has in the slightest blunted the appetite for crack and heroin.
The Mexico issue is that they have an insecure northern border with a country with lax gun control, so their criminals can easily circumvent their own fairly strict gun control laws. So to hear an American complain about guns coming across the border is beyond ironic.
I don't think the flow is going to be reversed that easily, we have a ways to go between criminal demand in the US for Mexican firearms is anywhere near the criminal demand in Mexico, much less higher. It doesn't really make sense to predicate gun control on border security, since you can phase in gun control long before border security issues impinge on the number of illegal guns in the US.
It's a point that's been made over and over and over. Making guns illegal will only take the guns out of the hands of honest people. There will always be a ready supply of illegal contraband (guns, ammo, drugs, whatever people want) coming up from Mexico until such time as that border is secured strongly enough to stop the flow.
And if you know of a good way to secure thousands of miles of this...
... then I'm sure the administration would love to talk to you.