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Your SOL are not stored on your hardware wallet. It just contains the keys for all your wallets for all the cryptos you use.
Ledger or any other type of wallet use the keys to interface with wallets. Wallets are just a program that send commands to the network specific to a crypto and ask nodes to write your transaction in the Blockchain.
Now ledger has some app compatible with the ledger app directly. So you can see your amounts directly in the ledger app.
For some crypto, you will need to use another UI because ledger doesn’t not have yet a built-in app integrated within the ledger app.
Hence the SolFlare app that you will use. The SolFlare wallet app will request your ledger to securely share the key so you can check your balance and interact with it.
But it will still be secure since you need to validate each transaction wiith the ledger hardware