HP's are instantaneous. As soon as you have an HP from an app, it will be visible on a subsequent pull on the same bureau. "Hiding" HPs or new accounts doesn't really work now, regardless, as almost all lenders will monitor your reports w/ SPs after approval and will shut down a card if they see credit-seeking activity that spooks them.
As to your specific case, I'd generally recommend waiting 6 mo's to a year between apps when building from a young, thin profile. But if you really want both, you could apply for the one that's more important first, and then the other one second. For the one you apply for second, you may get approved or you may get denied, but, if approved, you've got both cards, and, if denied, you were going to try again in 6-12 mo's anyway.
In my case I do this often. Not so much to hide the hard pull because I know that will show up. However, I feel that my score is not affected until the day after the hard pull. I could be wrong but this has worked for me. So I want to get in as many pulls as possible before that score changes.
I also feel I get less of a ding from multiple pulls on the same day, same bureau.
What you are describing might work depending on the lender. First both lenders will need to access different bureau's for their reports. Then they will need to not access any secondary bureau's like Sagestream. Only then would it work. Nowadays lots of lenders have started using the same sources of info and some lenders like to ask everyone. Capital One is considered the least liked because of their triple pull per new account. As for afterward the accounts grow at the same time so your score recovers faster. HP's show up instantly or almost instantly on their bureau. TransUnion , Experian , and Equifax have separate records.
In the case of your idea I would guess your at 2/24 inquiries at worst since you did not say which HP failed to get you an account and they do not clear for 2 years. Your best best would be to figure out which one you like more and apply in that order or the order of best approval which is AmEx and then Fidelity. That way you enter the AmEx system faster and that will mean they will try to SP any additional account after your first. Fidelity knows they are an afterthought so they will be easy on you for approval. In the end you probably will get both unless you do not have enough income.
