Praise be to Allah.
What appears to be the case is that the Sunnah of istikhaarah cannot be done by praying just one rak‘ah, because of the report narrated by Jaabir ibn ‘Abdullah (may Allah be pleased with him) who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) used to teach his companions to make istikhaarah in all things, just as he used to teach them soorahs from the Qur’aan. He said: ‘If any one of you is concerned about a decision he has to make, then let him pray two rak‘ahs of non-obligatory prayer…
Narrated by al-Bukhaari, 1166.
Al-Bujayrami (may Allah have mercy on him) said: The words of the Prophet (blessings and peace of Allah be upon him) referring to two rak‘ahs of istikhaarah indicate that it cannot be done with just one rak‘ah.
End quote from Tuhfat al-Habeeb ‘ala Sharh al-Khateeb, 1/428
Al-‘Ayni (may Allah have mercy on him) said: The evidence indicates that the Sunnah in istikhaarah is to pray two rak‘ahs, therefore one rak‘ah is not acceptable for istikhaarah.
End quote from ‘Umdat al-Qaari’ Sharh Saheeh al-Bukhaari, 11/385
Ash-Shawkaani (may Allah have mercy on him) said: The words “let him pray two rak‘ahs” indicate that the Sunnah in istikhaarah is to make it two rak‘ahs, so one rak ‘ah is not acceptable.
End quote from Nayl al-Awtaar, 3/88.