How can I save multiple checkboxes to member profiles?

Yes, you can do it by code, but you will need several steps to go, till you can achieve your aim.

What you should know for your project?

  1. How to use Velo-APIs ? https://www.wix.com/velo/reference/api-overview

  2. How to get data out from DB? Your data will be surelly stored in a DB.
    https://www.wix.com/velo/reference/wix-data/query

  3. How to save data back to DB?
    https://www.wix.com/velo/reference/wix-data/save
    …or…
    https://www.wix.com/velo/reference/wix-data/bulksave

  4. How to get data of a person (user)?
    https://www.wix.com/velo/reference/wix-users/currentuser

And this is perhaps not the fully way of doing to get your aim.
As you can see, you will have to go several steps. Do everything step by step.

  1. Do you have already a DATABASE ?

If YES:

Try to get some data out of this DB,…

import wixData from 'wix-data';

$w.onReady(()=> {myFirstFunction()})

function myFirstFunction(){
   wixData.query("myCollection") //<---change here the name of your DATABASE
       .find()
       .then( (results) => {
          if(results.items.length > 0) {
             let firstItem = results.items[0]; 
             console.log(results.items)
             console.log(firstItem)
          }   
          else {      }
       })
       .catch( (err) => {
       let errorMsg = err;
   });
}

You can test this code in the Preview-Mode in your Wix-Editor (take a look onto the CONSOLE, on the bottom of the screen.
Or use for example google-chrome and press F-12 and navigate to CONSOLE, to see the output-results.

Your first step is done, you were able to read data out of a DATABASE.