I am both a Jamaican and US citizen and I am traveling to Russia for my studies. I have my student visa in my Jamaican passport. The details of my trip are as follows: I was going to fly to London Heathrow on one airline and then catch another plane to Russia from there. Can I use my American passport for the first leg to London and then use my student visa for the second leg?
Assuming you flying direct from Kingston to Russia and only transferring in London, my suspicion is that you would only have a single opportunity to show a passport. You would only show the passport if you left the sterile area- and hence were entering the UK. At that point, you are operating as two distinct and unrelated trips. You can show which ever passport you want for either of your two distinct journeys.
Even on separate airlines, it is simply a matter of arriving at LHR and changing gates. You only go through immigration as you are leaving.
You will show your passport in Kingston and will be asked what your final destination is. If you say London or Russia, they will do a cursory check for the appropriate visa, but no official record is being made. When you get to Russia, they will check for real- and that is the visa that goes into the system.
Unless if you leave Heathrow, you only get one chance. If you do leave Heathrow, the passport you show to get to the UK has no bearing on the one you show in Russia. They completely unrelated trips from a governmental perspective.
And if you have no valid visa, say hi to Edward Snowden for me...
You don't use a passport for a "leg" of the trip. You use a passport to enter a particular country and to leave a particular country (if it has exit checks).
You should always enter and exit a country with the same passport. But the passport you use to exit the country at the start of the "leg" and the passport you use to enter the country at the end of the "leg" don't have to be the same.
The UK doesn't currently have exit checks, so the entering and exiting it with the same passport is somewhat moot.
For the airline, you should generally provide them with the documents that allow you to enter the destination country, because that's what the airline cares about because they're liable to bring you back if you can't enter. But for the countries that don't have an exit check and don't have a form you have to turn in on departing, you should also provide the airline with the passport information you used to enter (which may mean you provide them with two passports) in order to match up entry and departure records for that country.