Flight Crew reported a GEAR TILT Message showed on the EICAS with the respective aural warning on take off. During approach to landing at destination airport; the #4 Engine flamed out. Flight crew continued to landing.

Narrative

After takeoff; as soon as we had a positive rate of climb; First Officer (FO) commanded the landing gear up. As I went to bring the gear lever up; it did not move to the up position; I looked at the EICAS and the GEAR TILT message showed on the EICAS with the respective aural warning; at this time I commanded to engage the center autopilot and to open the speed intervention window on the Mode Control Panel; in order to limit the air speed to 250 kts. while the flaps were being retracted.As soon as the flaps were retracted and the speed was within the limits; I took control of the aircraft and communications. I asked FO to get the QRH procedure for the GEAR TILT issue. I advised ATC that we had an issue with the landing gear and requested to maintain FL 200; after FO finished the QRH procedures and the gear could not be retracted; I asked FO to phone patch Operations so we could figure out the fuel and flight plan amendment to continue to destination per the QRH performance inflight. We collectively decided to continue to destination and we used the QRH performance at FL 250. After Operations calculated the amended flight plan and fuel burn from our current position (time remaining; 1 hour 27 minutes & a distance of 500 NM). The decision to continue was based mainly on the amount of fuel onboard (45;000 Kilograms); at the time of the re dispatch calculated fuel remaining it was shown to be 18;000 Kilograms at landing; giving us a fuel burn of 27;000 Kilograms with all the gear extended. Once we got to top of climb; the fuel burn calculation was slightly higher than planned.With ZZZ Approach and beginning the approach with the left downwind leg to Runway XXR; we were instructed to change to Runway XXL due to an emergency aircraft ahead of us who were approaching Runway XXL. At this point and time; the first alert comes on stating a Warning on Engine Number 4; then Engine Number 4 started to fluctuate. I then proceeded to make the proper corrections and called for Engine Number 4 flame out QRH procedure. Then; the fuel press on Engine Number 1 EICAS MSG comes on with an aural warning. ATC was giving instructions to all aircraft that there was a priority situation in progress and were told to hold all aircraft arriving. We informed the Tower that we were having an issue with an engine losing thrust. FO by recall turned all fuel pumps on; the engine restarted but then shut down about a minute later. ATC gave us a vector to put us 15 miles behind the emergency aircraft ahead of us. When we started turning on final to intercept the localizer; the fuel press on Engine Number 4 EICAS MSG came on and the engine shut down; we were at 1;500 ft.; 15 or 12 miles out when this happened. At that point we were committed to put the aircraft on the ground safely. We [requested priority handling] right away. We tried to vacate the Runway but couldn't because the steering was inoperative. There was no time to run any other checklists. Then established on the ILS that I had to park on the Runway for about 45 minutes to get towed for our fuel; we were more or less at 12;800 Kilograms. Is hard to comprehend what happened. We took off with the fuel system in fuel tank to engine with 48;600 Kilograms of fuel for a 01:24 hour flight; enough fuel without any conditions. After we took off and had the gear tilt issue; we called the Company and made all the calculations in our performance. At the beginning; this gave us a fuel of 18;100 Kilograms for landing. As we were getting closer it started to drop a little but we still had the fuel. The performance took us the check the fuel flow and the total fuel to make the proper calculations and at the time of the approach we didn't understand why the engine was fluctuating. I asked the FO to check as I was flying and talking to ATC when I notice he was turning all the fuel pumps on and the cross feed valves on.Even doing the checklists; we had the proper calculations; total fuel and fuel flow; it never took us to monitor the fuel system to check each tank; and the system was tank to engine so all tanks should had burn the same the fuel flow was 5 on each engine.