Not likely, Redbeard.
The grievance that led to war was the Royal Navy's efforts to blockade Napoleonic Europe. No Napoleon and no war, no War of 1812.
Had the war been lost badly, as it could have been, we could assume a loss of fishing rights, perhaps a third of Maine, and most of Indiana/Illinois and all of Michigan and Wisconsin lost. Then we could also assume a dramatic change in the US's posture in the world. For one thing, all the free settlers would have had to go elsewhere, quite probably doing real harm to southern unity on slavery. Likely Kentucky and Tennessee become much less interested in slavery, perhaps Alabama and Mississippi divided on a north/south basis with the northern one also free. Inevitably a revenge war would take place, with the US having a substantial fleet and army.
Needless to say, secession would become much less likely, given a powerful military(50 to 100 thousand) at the president's disposal.
Around the early 1840s I would predict an increasing stream of settlers, if not earlier, into the lost Midwest, putting the Indians under heavy pressure. Most likely when war emerges, the Royal Navy can establish a blockade and win any fleet action, but a substantial US Navy and harbor fortifications obstructs many landing attempts. Meanwhile, the US Army not only crushes the Indians but takes most of Canada. The British, in effect, are sending forces in piecemeal, and lose much of their standing force early. Further, their entire army is probably little stronger than the US, and is scattered around the world.
If this erupts during the 1848 crisis, the great Indian Mutiny(India, not here), or the Crimean War, England likely cedes everything gained in 1812 and probably parts of Canada or even substantial reparations. The grudge would last even longer, especially if the British felt they only lost due to treachery on the part of an attacker while they were already heavily engaged.
If not, it still goes the way of the US, for UK is not fighting a long and expensive war, with US privateers no doubt wrecking havoc, all for an Indian buffer zone. In this case, the US in effect STILL gains what it lost plus likely a few bits more of land. Perhaps ALL of Oregon territory.
Either way, there is bad blood for a long time.
One could also postulate a long border war after 1812, with the Indians being hit hard early and the British increasingly taking losses for what was nothing more than a buffer state. Truthfully, although much better than the US, Canada and UK were still prone to dump the natives whenever it was convenient.
Developments in armaments are up to you folks.