Can fluoride be absorbed through the inside of the mouth?

No. Fluoride is usually not absorbed through mouth mucosa. Fluoride varnish, once applied, sticks firmly to the enamel and doesn't get absorbed in the body through one's mouth. Otherwise, you will need to take Fluoride drops or pills to supply necessary Fluoride to your body. Fluoride containing mouth washes also don't contribute to Fluoride concentration in your body unless accidentally swallowed.
No. No, Fluoride is not absorbed into the body through the oral mucosa. Fluoride can be absorbed through the digestive system when it is swallowed in water or supplements. Remember, Fluoride is an essential trace mineral in the body for strengthening enamel.
No. No, Fluoride is not absorbed through the skin inside your mouth. Some Fluoride may be retained on the surface of your oral mucosa, where it is then available to help re-mineralize your teeth after acid exposure, but it is not absorbed.