That's しょきか.
In a compound word, the last syllable of the first kanji changes to the double consonant under certain conditions. This phenomenon is called 促音化[そくおんか] in a broad sense. 期 is a single syllable kanji. 促音化 doesn't occur in this case.
Here's interesting examples.
石化[せっか]
化石化[かせきか]
悪化[あっか]
再悪化[さいあっか]
最悪化[さいあくか]
化石化 and 最悪化 are made from "化石 + 化" and "最悪 + 化", respectively, therefore き / く doesn't change to っ. Whereas 再悪化 is from "再 + 悪化", that's why it's pronounced さいあっか.