For travellers from the UK, you are fortunate in having a website available that gives you up to date and reliable answers to all your travel money needs. That site is Moneysavingexpert.

Normally buying foreign cash is not the best way to deal with travel spending. Using the right debit and credit cards while travelling is the best way. However, many people like to have a little local currency in their pocket when arriving in a foreign country. If that is what you are talking about, not a large amount, then you can find where you will get the best rate here: https://travelmoney.moneysavingexpert.com/

You are not going to get the best rate anywhere using Amex to pay. As you will see on the above link, your best choice appears to be the Travel Money Club if they will accept payment by Amex card. But it will not get you the best rate, only the best rate using an Amex card to pay. Again, if they accept Amex. You will have to drill down in their site to find that out using a 'dummy' transaction.