I've multiple wallets and I was wondering if I keep transferring bitcoins among these wallets (my own wallets ) will that eventually consume all my coins (keep paying fees )?
Obviously, yes, it will, due to every transaction need a transaction fee. Not unless if you use a wallet such coinbase and send to another coinbase wallet which are hosted web wallets that never as ask any fees in transferring funds.
But for what reason you would do that?