Perhaps you should check the fan / light fixture for loose wiring or a poor connection, even in the lamp socket. If the lamp receives a constant power supply, there is no reason for flickering. And no common switch or timer should do what you describe. But a loose connection in the fixture, constantly subject to vibrations of the fan motor, might cause very short disconnections. If that is happening, it would not make a regular incandescent bulb flicker because their hot filaments do not respond to very short power changes. But an LED can respond quickly.
Try these three tests.
1. Temporarily replace the LED with a regular incandescent bulb. If that does not flicker, then you have confirmed that the flicker is caused by very short power changes.
2. CAUTION! Be very careful with this, and maybe do NOT try this if you are no familiar with handing live electrical circuits. At the timer switch, rig a temporary bypass of the switch so that the fan / light gets power and turns on when the timer is OFF. See if that changes anything with the LED lamp. If the flicker still happens, the problem is in the fixture. If the bypass eliminates the flicker, the cause is in the timer.
3. AGAIN, CAUTION! IF it is possible, at the fixture disconnect the power lead to the fan motor so it can't run. Turn on via the timer switch. If the flicker disappears when the motor is stopped, but happens when the motor runs, then the motor vibrations may be contributing to the problem., as I suggested at first.
One last possibility to consider (relates also to that last test I suggested). The fan MOTOR is NOT an "incandescent lamp" device. That timer may not have been designed or rated for such a load. As a start, check the electrical rating of that timer - particularly, the Amps, maybe the Watts. If it is low (say, less that 5 Amps or 600 W), it may not be suitable for that application.