How to get values of multiple aliases without introducing callback hell in Cypress?

You can do this:

it('test', () => {
    cy.wrap('foo').as('foo');
    cy.wrap('bar').as('bar');
    cy.wrap('baz').as('baz');

    const values = [];
    cy.get('@foo').then( val => {
        values.push(val);
        return cy.get('@bar');
    }).then( val => {
        values.push(val);
        return cy.get('@baz');
    }).then( val => {
        values.push(val);
        someFunc(...values);
    });
});

Or you can use this helper I cobbled together (put it in your support/index.js):

const chainStart = Symbol();
cy.all = function ( ...commands ) {
    const _           = Cypress._;
    const chain       = cy.wrap(null, { log: false });
    const stopCommand = _.find( cy.queue.commands, {
        attributes: { chainerId: chain.chainerId }
    });
    const startCommand = _.find( cy.queue.commands, {
        attributes: { chainerId: commands[0].chainerId }
    });
    const p = chain.then(() => {
        return _( commands )
            .map( cmd => {
                return cmd[chainStart]
                    ? cmd[chainStart].attributes
                    : _.find( cy.queue.commands, {
                        attributes: { chainerId: cmd.chainerId }
                    }).attributes;
            })
            .concat(stopCommand.attributes)
            .slice(1)
            .flatMap( cmd => {
                return cmd.prev.get('subject');
            })
            .value();
    });
    p[chainStart] = startCommand;
    return p;
}

and use it like so:

it('test', () => {

    cy.wrap('one').as('one');
    cy.wrap('two').as('two');
    cy.wrap('three').as('three');

    cy.all(
        cy.get(`@one`),
        cy.get(`@two`),
        cy.get(`@three`)
    ).then( values => {
        someFunc(...values);
    });
});

One different solution which is custom developed by Mr. Nicholas Boll, where you will get aliases as an array using custom commands createAlias/ getAliases,

// get many aliases - API is similar to Promise.all
cy.getAliases([getFoo, getBar, getOne]).then(([foo, bar, one]) => {
  foo // string
  bar // string
  one // number
  console.log(foo, bar, one) // logs 'foo', 'bar', 1
})

Here is the complete details in his blog - https://medium.com/@NicholasBoll/cypress-io-making-aliases-type-safe-b6f5db07d580

Code reference - https://github.com/NicholasBoll/cypress-example-todomvc/tree/feat/type-safe-alias