I can't multitask very well. But I can pipeline very well.
Lineup tasks so that they're very efficiently done. Exploit geographic locality. Plan out the day so you know what can be batched together.
I brush my teeth in the shower, simply because it's easier. There's already water there. And you have to let your shampoo soak in any way. That's just pipelining
Having a task list is great, you can use Google tasks, or a calendar app, or just a notepad. You don't have to respond to every message as soon as it comes in. You can batch up all your instant messages till the end of the day and respond to them once a day. That's fine.
Don't let your email inbox be a task list. Keep your inbox empty at all times. Read it and then decide if it needs to be dealt with, make a task. The needs a response send the response immediately even if it's I'll get back to you if the data later. Then you'll have a workable task list to batch and pipeline for day.
Don't let other people's asynchronous communication interrupt you. Unless there's a phone call, it can wait. And if people are calling you you better make it clear to them it has to be an emergency.