I am thinking of transferring my bitcoins from BlockChain to CoinBase
is there any transaction fee invloved?
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There will be a fee because the transaction will be broadcast and saved to the Bitcoin blockchain. You can probably start the transfer process on Blockchain and they will show you a preview of what they estimate the fee to be. It all depends on the size (in bytes) of the transaction. For more see their explanation about bitcoin fees
Moving bitcoins from one exchange to another requires transacting on the Bitcoin blockchain which is different than the trading fees implemented by exchanges.
The price of the fee depends on the size of the transaction (in bytes), and speed of the transaction confirmation depends on satoshis per byte. The more you pay, the faster confirmation time you can get.
Estimatefee.com is one tool to estimate bitcoin fees.