Can I simply apply for a chargeback on my credit card if my flight was cancelled and I'm unable to reach the airline?

With respect to Tor-Einar's more general answer, the position is a little more comfortable in the UK. I accept that the OP isn't there, but we're here for everyone, surely?

Section 75 of the Consumer Credit Act 1974 provides that the card issuer is jointly and severally liable to the card holder for claims in respect of misrepresentation or breach of contract. As Which? (the UK's largest consumer protection organisation) more readably summarises matters,

This means it is just as responsible as the retailer or trader for the goods or service supplied, allowing you to also put your claim to the credit card company.

They go on to note that

You don't have to reach a stalemate with the retailer or trader before you can contact your credit card provider - you can make a claim to both the retailer and credit card provider simultaneously, although you can't recover your losses from both.

It's clear from other writings here that you have a statutory entitlement to a refund, and nothing is said about the acceptance of vouchers being mandatory.

So as I read it, in the UK you are perfectly entitled to try ringing BA and failing to get through, then getting on the phone to your card issuer and requesting a refund. This is in no way a misuse of the system; it is your entitlement as a credit card holder.

Note that you aren't concerned about chargebacks. It is likely that your card issuer will seek to recover from BA any moneys refunded to you, very possibly by the chargeback mechanism, but that is a matter between them and BA. What you want is a refund, plain and simple.

This is a variation of a question that came up often enough. In practice, a chargeback will currently be your only recourse in cases like this.

For obvious reasons, airlines do not want to give refunds currently, and are even pushing for legislation that would allow them to give out vouchers instead of refunds, and delay the actual payout for up to a year.

However, at this time the EU regulation still stands: You are entitled to a refund if your flight is cancelled in all cases - even if the cancellation is not under the airline's control. Nevertheless, the airlines won't pay; and I assume that even if they agree that you are right they may simply try to delay payment until after the crisis.

If they do not refund you, you can request a chargeback. Here's guidance from the ING, one of the large banks in Germany. It's in German, but in a nutshell:

• You have to talk to the company (airline) first
• If they offer a voucher, the bank suggest that you take it
• If you do not want a voucher, you need to request a refund from the company/airline
• If they either refuse, or do not react, or do not refund within 30 days, then you can ask to initiate a chargeback

Best to keep all the documentation of your attempts to resolve the situation (e.g. emails sent).

Note: While the OP has a US card, chargeback rules don't vary wildly and you are entitled to a refund if the other party has no legal right to the payment; also the EU regulations for refunds apply in this case regardless of the nationality of the passenger.

Good for the OP that they got the situation resolved.

It will depend on the details in the contract between yourself and your bank and/or consumer protection legislation in the applicable jurisdiction.

Chargebacks' main intention is to prevent credit card fraud and to reverse unauthorized charges to your card. They are not necessarily rightful, just because the merchant doesn't provide the product or service you ment to pay for. The only time I disputed a credit card charge, I had to sign a statutory declaration that I hadn't authorized it. My bank would not allow me to reverse a credit card charge which I actually authorized, just because I allegedly not got what I have paid for. Making a wrongful statutory declaration may have quite severe consequences for you and is here in Germany punishable with up to three years imprisonment.

It is however not uncommon that banks or consumer protection legislation allow a more broader use of chargebacks. It may also be a legal argument that your authorization was bound to the condition that you actually get what you pay for.

With cancellations caused by the corona situation, the legal aspects are not always obvious and it is unfortunately not self-evident that an airline is obligated to compensate you for a cancelled flight. I assume (based on the airlines) that your flights are covered by the EU Flight Compensation Regulation, but I am not 100% sure what the airlines are obligated to in case of force majeure. If the airline is not legally obligated to pay you back in cash for the cancelled flight and you reverse the credit card charge, you must assume that the airline will find a different way to reach out to you and present a claim for the ticket price and additionally whatever they feel entitled to for such an 'extra service'.

Given that I'm unable to reach the airline at this moment, can I just apply for a chargeback on my credit card?

When you phrase it like that, no. To make a chargeback, you have to first give them a reasonable opportunity to resolve the issue directly with you. Not being able to reach them "at the moment" does not justify a chargeback. Given the extraordinary circumstances, some leeway is due.

On the other hand, prior to this you present conditions beyond mere not being able to reach them "at the moment". Five days is pushing it, although, again, given the circumstances the generous thing to do would be to give them a bit more time. You also say that the other airline is requiring people to call, and in this day and age, I find requiring a phone call to be unjustified. They deserve some of the blame due to their insistence on using twentieth century technology, but even if they were using a web-based submission system, they would still likely have a backlog.