Learn Swedish: Sverige är inte lika platt som Danmark.

While English repeats the word "as" (as flat as), Swedish uses two different words. Lika means "equally" and som means "as" or "like". So, lika platt som literally translates to "equally flat as".

Could I use än instead of som in this sentence?

No. You always pair lika (equally/as) with som (as). You only use än (than) when you have a comparative adjective. For example, you would use än if you said Danmark är plattare än Sverige (Denmark is flatter than Sweden).

Why isn't the adjective in the comparative form, like plattare (flatter)?

With the lika ... som structure, you always use the basic form of the adjective (platt). This is exactly like English, where you say "as flat as", not "as flatter as".

Countries are usually ett words. Shouldn't platt get an extra -t at the end to match Sverige?

You are right that countries are treated as ett (neuter) words, which usually means adding a -t to the describing adjective (for example, Sverige är vackert). However, because platt already ends in a double -tt, its neuter form stays exactly the same as its base form!