what exactly is flow involved in transfer of a bitcoin from my account on one exchange to someone else's on another exchange?
Your intended recipient will have requested exchange 2 to generate a receiving address for your intended transaction. This receiving address is owned by exchange 2. The recipient will pass this address to you in any way that suits them (QR-code, whatsapp, email, etc)
The first exchange deducts an amount from your account balance. This has no effect on the Bitcoin network because you own no Bitcoin so far as the Bitcoin network is concerned.
The first exchange typically batches together a set of several tens, hundreds or thousands of customer transactions it needs to make where recipients are not its customers. It combines all these requested customer transactions into one single bitcoin transaction with hundreds or thousands of different recipients (outputs). One output of that combined transaction will pay an amount to an address owned by exchange 2 which you have requested exchange 1 to pay.
The first exchange transmits copies of the proposed (unconfirmed) Bitcoin transaction to a handful of Bitcoin nodes (its peers). Copies multiply and diffuse across the Bitcoin network, eventually some copies of this proposed transaction reach miners.
A miner successfully includes that transaction into a block, usually with thousands of other transactions. It transmits copies of the new block to a handful of peers.
The second exchange eventually receives a copy the block, thereby discovering it has received the amount you specified.
From the receiving address (and maybe the amount) it can reconcile this received amount against an expected payment to one of it's customers.
The second exchange credits an amount to the account of one of its customers. This part is nothing to do with the Bitcoin network.
Only the numbered items in the above list are actual Bitcoin events. The other items don't really involve any real Bitcoin.
The Bitcoin network has no record of your money or of the recipient's because you are both using a custodial service and neither of you has any money as far as the Bitcoin network knows.
for example: is there a transfer from my account (regular, custodial) to main exchange account for pooling purposes?
The Bitcoin network has no accounts.
What exchanges do with their customer accounts is of no relevance to the Bitcoin network. It is up to each exchange how they move numbers around internally.
Exchanges can internally shuffle around the IOU's and promises which they have issued to customers in order to maintain their customer's illusion that the customer owns money (customers don't). The exchanges often don't need to move any real money around. The reality is that once you give money to someone else (the exchange) you no longer own or possess that money. You only possess an expectation that the other person (the exchange) will give you back some money if you ask it.
will be a transfer first from cold wallet (occassionaly) to hot wallet ...
Probably not, but maybe so if the exchange's hot-wallet "balance" would otherwise fall below some threshold the exchange sets. This is a matter for the exchange to manage however it wants.
...that i know of
You only need to know that there is a transaction that pays the specified amount to the specified address. You don't need to know where that money came from.