Charge cards are not installment accounts of any kind. Nor are they treated in the same way as revolving accounts are -- for example they do not help you with your CC utilization in FICO 8 or 9. Very old scoring models (for example the Experian mortgage model) may take the High Balance field (highest balance you have ever had on the card) and use that as a proxy for credit limit -- and in such a model they would be counted toward revolving utilization.
I am pretty sure that they do count toward "number of accounts with a positive balance" -- FICO doesn't like it when you have many accounts showing a balance (even if it is a small balance).
There has been some guesswork here on the forums that perhaps "charge cards" are considered as one additional type of credit by FICO in its "credit mix" assessment. Thus if a person has a huge love of a particular Amex charge card (just for the benefits he perceives) there might be also be small tangential scoring benefit from having it. But nobody should get a charge card solely to chase that phantom benefit.
As far as the best way to iimprove your credit mix (and also get an extra 30 points to your FICO 8 score) I would suggest the Share Secured Loan Technique.
Since you are curious how your charge cards will appear on Credit Karma's reports, that's pretty easy to solve. Sign up with Credit Karma.
Finally, have you done the math and confirmed that the annual fees you are paying for these cards are worth it to you? It's often the case that you can net more money by using no annual fee cards.
PS. You ask what credit bureaus your Amex charge cards will report to. The answer is all three. That you are asking the question suggests, however, that you have not pulled your reports at all three bureaus. You should do that. There are free tools for doing so.
