The KJV is in the minority, if not unique, in its use of "charity" as opposed to "love" in its translation of that passage. In particular there are two forms of love being talked about here; in verse one the Amplified Version defines it as "that reasoning, intentional, spiritual devotion such as is inspired by God's love for and in us" and in the latter verses simply as "God's love in me". So in this answer I talk about "love" as opposed to "charity" - particularly to avoid confusion as verse 3 talks about both the practice of charity (the practice of benevolent giving and caring) and the virtue of charity (the Christian theological concept of unlimited love and kindness).
The first two verses are talking about what a person contributes through particular actions, and the third is concerned with what a person gains through particular actions. The important thing here from a Sola Fide perspective is that these are three distinct sentences. They are related to one another, but they do not say "If I have faith and not love, I gain nothing."
Verse 1 is self explanatory: speaking various languages, including the tongues of angels, without love is just noise.
Verse 2: A person is useless without love, even if they have the ability to prophesy, a deep understanding of mysteries, encyclopaedic knowledge of everything, and sufficient faith to move mountains. Note that it doesn't say such a person is not saved; it just says they contribute nothing of use. This is the only verse that talks about faith, but it doesn't talk about salvation; it says that it's possible to have faith and not contribute anything of use, but it doesn't say that you need more than faith to be saved.
Verse 3 is the only one that relates to salvation, because it talks about what a person gains. It says that without love, giving away all our possessions and even giving our lives, gives us nothing. In other words we are not saved by good works. Note that verse 3 does not mention faith in God; it does not say "if you have faith but not love, you are not saved" it says " if you do good works without love, you don't gain anything". Therefore it doesn't negate the notion that faith is sufficient for salvation.