Is it possible to transfer BitCoins from BlockChain to CoinBase?is there any transaction fee invloved? I am thinking of transferring my bitcoins from BlockChain to CoinBase

is there any transaction fee invloved?
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