My best use for the MiG-31 was on the WW3 server, where I managed to fly from the IFF4 base to the middle island in less than a minute, and managed to get one lucky missile on my target while streaking low over the island at 750 kts. It took me just over 3 minutes to execute the whole operation, take-off to landing. No other aircraft can intercept like this one can. It gets you before you know it, and it hits you hard. Then it's gone before you can get a comeback on it. Hardly any other plane can hit-and-run like that.
Recommended use: Load it up with a mix of AIM-9s and AIM-120s, then go up to your target and give it a good hard whack with the missiles. If you are in hostile territory and still have missiles to get him a second time, do a wide loop over nearby friendly/neutral territory, then when he has respawn and is near to you, pull out of it, fly straight at him, and give him another whack with the missiles. If you run out of missiles, just full AB RTB outta there.
TL;DR - How to use a MiG-25/31 in 6 easy steps (credits to Gunny):
1. Wait for intruders to get within danger range of airbase
2. Take off with fully-armed MiG with 50-70% fuel
3. Take out as many hostiles as possible.
4. RTB at high-speed.
5.1. Reload and refuel to full armament and 50-70% fuel.
5.2. If any other MiG25/31s are ready to take off, send them out one by one, putting out one as soon as another gets back. Don't send them all out at once because they will end up in a dogfight and get outmaneuvered.
6. Repeat steps 2-5.2 as many times as needed.
It's best to have about 3-4 because the can just go in a cycle of taking off, firing, then calling another one out as soon as the first is exhausted of armament. This way the enemy won't have any windows of time to attack the base while the MiGs are reloading and refueling.
Combatting a MiG-25/31: It is very difficult to out-run a MiG-25 or -31 in straight flight, so if you want to combat one, make sure you use a lot of evasive tactics on it, and if it is trying to fly straight but somewhat perpendicular to you, use its low maneuverability to your advantage (it turns
only slightly faster than an airliner even with trim) and cut in front of it, looping around the front and sides if necessary. Flying head on will not work for if you miss it, it can simply scream off into the horizon even before you can turn around. Always keep in mind that a straight chase will not work for as hardly any fighter jet can catch up to a straight-cruising MiG-25/31, and forcing it into a tight-turn dogfight will out it at a severe disadvantage due to its low maneuverability.
Any other notes for the MiG-25/31 can be posted here.