There are only really two "combos" to be aware of. The first one is to use your E before you ult. The ghost that spawns from a connecting e counts as an additional champion and will spawn a tentacle when hit by ult just like an enemy champion would. You can use this to dish out surprising amounts of damage and win most level 6 fights (provided you're not significantly far behind).

The second combo takes a lot of quick thinking. Illaoi's ult has a two-part animation. In the first half, she jumps up into the air, preparing to slam down onto the ground. The second half is when she starts falling from the air to slam to the ground. Between her ascending and descending animation, there is a brief pause where she is suspended mid-air (half a second at the most). During this suspended state, flash will relocate you as normal, which you can use to surprise the enemy team. This one requires prep or quick thinking. If the enemy adc is just out of range, try and land an e on someone and push r. Once you hit r, the second you go up into the air, flash deeper into the enemy team. Tentacles will spawn based off the number of enemies hit when you actually slam the ground. You can use this to usually win a fight easily.