The "colonists" (assuming you mean the 13 "American" colonies) never took Florida; the Spanish did. Then the British gave it back to them.

In 1763 the end of the French-Indian war saw the Spanish trade Florida for Caribbean lands (Cuba) taken by the British. It would remain British unoffically until 1781, when the Spanish took it as part of the American Revolutionary War. At the end of the war in 1783, the British traded it back to the Spanish. In the Revolution, Nova Scotia is known as the place Loyalists went with thousands going there. The number two destination for those citizens remaining with the crown ideologically was St Augustine, Florida. After the Declaration of Independence was issued, Samuel Adams and John Hancock - President of the Continental Convention (kinda like Speaker of the House) - were burned in effigy in the streets of that city. It wouldn't be until the Spanish became involved and brought war to Florida that anything impactful would happen there as the colonists were far too busy in occupied Georgia and battleground South Carolina to do anything with Florida. Georgia did attempt three times to invade Florida, the last being the most successful but really only reaching the St Mary's River. An interesting side note is that Button Gwinett, signer of the Declaration of Independence, was killed over the failed invasion. The second invasion was a debate between him and Lachlan McIntosh and after it failed they dueled over it. There days after being shot, Gwinett, namesake of the Atlanta adjacent county of Gwinett, Georgia, died. McIntosh was kicked out of the GA militia and sent to join Washington at Valley Forge as a result.

It remained a Spanish territory until J.Q. Adams negotiated to buy it in 1819 in the Adams-Onís Treaty (or Florida Purchase). We would assume some 5M$ in claims by Americans against the Spanish and take the land in exchange. In 1822 it officially happened and became Florida Territory, later achieving statehood (in the 1840s).