The correct reading is れんが, with both kanji using on'yomi. 連 (れん) is standard, and 歌 (が) is its on'yomi with dakuten, common in compounds like this. Incorrectly reading 歌 as か without dakuten, or as け/げ, are common mistakes. It is a traditional Japanese collaborative poetry form where multiple poets take turns composing alternating stanzas.

「連」は「れん」、歌は熟語では「が」と音読みします。「歌」を「か」と濁らずに読んだり、「け」や「げ」と読むのは間違いです。複数の歌人が交互に句を詠み継いでいく日本の伝統的な詩歌の形式です。