SANKHAYANA is same as shAnkhAyana as spelled in Sanskrit. We have to first see the lineage of this great Vedic rishi. Chapter 15 of the shAnkhAyana Aranyaka presents the following
atha vaMshaH| [This is the lineage]
om namo brahmaNe nama AchAryebhyaH| gunAkhyAc chANkhAyanAd asamAbhir adhItam | guNAkhyaH shAnkhAyanaH kaholA(La)t kaushItakeH | kahola(La)H kaushItakir uddAlakAd AruNeH | uddAlaka AruNiH priyavratAt saumApeH | priyavrataH saumApiH somapAt | somapaH saumAt prAtiveshyAt | saumaH prAtiveshyaH prativeshyAt | prativeshyo bRihaddivAt |
bRihaddivaH sumnayoH | sumnayur uddAlakAt |
uddAlako vishvamanasaH| vishvamanA vyashvAt |
vyashvaH sAkamshvAt | sAkamashvo devarAtAt |
devarAto vishvAmitrAt |vishvAmitra indrAt
indraH prajApateH | prajApatir brahmanaH |
brahmA svayambhuH | namo brahmaNe | namo brahmaNe || 15.1||
I think the list above is self-explanatory. It gives the lineage of teachers and pupils. The first teacher named is Gunakhya Shankhayana. He is the pupil of Kahola Kaushitaki, who is the pupil of Uddalaka Aruni, followed by Priyavrata Saumapi. Uddalaka is also mentioned to have disciples/teachers such as sumnayu and vishvamanasa.
Vishvamana to vyashva to sAkamashva to devarAta to vishvAmitrA to indra to prajApate to Brahma.
The Kahola Kausitakeya of the Brhadaranyaka Upanisad, iii, 5, 1, is presumably identical with the person named here while Uddalaka Aruni is well known to the Brhadaranyaka and Chandogya Upanisads and is a contemporary, according to tradition, of Yajnavalkya. Kausitaki is cited not only in the Aranyaka but also in the Brahmana as an authority, and is mentioned in both the Asvalayana and ShAnkhAyana Grhya Sutras
We can go to a little more detail to put this in context.
shAnkhAyana was a pupil of Kahola Kaushitaki, who was a pupil and son-in-law of UddAlaka Aruni, who was the contemporary of Videha King Janaka. UddAlaka Aruni father-teacher was Aruna Aupaveshi. Aruna (mentioned in Satapatha Brahmana) was the son of Upavesha (Brihadaranyaka Upanishad) and a contemporary of King Ashvapati Kaikeya. Patanchala Kāpya was also UddAlaka teacher.
The great Yajnavalkya (Brh.Up.6.3.15) as also sage Kausitaki (Sat Brh.11.4.12) to whose family the portions of the Kausitaki Brahmana are attributed, Proti Kausurubindi of Kausambi (Sat Brh. 12.2.213), and Sumnayu (ShAkhAyana Aranyaka -15.1) were at students of Uddalaka Aruni.
The Brihadaranyaka Upanishad (given below, 6.5.3) in its lineage of teachers lists generations of teachers.
yājñavalkya uddālakāt |uddālako ‘ruṇāt | aruṇa upaveśeḥ | upaveśiḥ kuśreḥ | kuśrir vājaśravasaḥ | vājaśravā jīhvāvato bādhyogāt | jīhvāvān bādhyogo ‘sitād vārṣagaṇāt | asito vārṣagaṇo haritāt kaśyapāt | haritaḥ kaśyapaḥ śilpāt kaśyapāt | śilpaḥ kaśyapaḥ kaśyapān naidhruveḥ | kaśyapo naidhruvir vācaḥ | vāg ambhiṇyāḥ | ambhiṇy ādityāt | ādityānīmāni śuklāni yajūṃṣi vājasaneyena yājñavalkyenākhyayante ||
According to this rendering, UddAlaka Aruni was the son of Aruna Aupavesi Gautama who was the son or disciple of Upavesa [and a contemporary of King Ashvapati Kaikeya] UddAlaka was a contemporary of Videha King Janaka. UddAlaka is famous for the discourses he imparted to his son Shvetaketu in the Chandogya upanishad. UddAlaka's daughter (Sujata) was married to his pupil (Kahola) and his grandson was Astavakra who spoke Astavakra Gita to King Janaka. The idea of giving the above explanation is to show that the lineages given in different Aranyakas and Upanishads match and have cross-references to the same name.
Coming to the point of Gotra, I can only say the following. UddAlaka belonged to the Gautama gotra. In the lineage of Vishwamitra, the followings were born, viz. Vaishwamitra (Madhucchanda), Devarat, Vaikruti, Galava, Vatanda, Shalanka, Abhaya, Ayataayan, Shyaamaayan, Yajnyavalaka, Jaabaala, Saindavaayana, Vaabhravya, Kareesha, Samsrutya, Ulupa, Auopahaava, Payoda, Janapaadapa, Kharabaacha, Halamaya, Saadhita, and Vaastukoushika. The Pravara of these Rishis is Vishwamitra, Devavrata and Uddaala.
shAnkhAyana gotra is only mentioned with the pravara ShankhyAyana: Vishwamitra, Aghamarshana, Devarata. Though Aghamarshana is not mentioned in Chapter 15 of the Aranyaka, this is a list of teachers and not of lineage. Further, the gotra is famous in Gujarat and they descendants maintain the Rannade temple in Gujarat and also live in Himachal Pradesh. As they don't marry people born in Visvamitra gotra, this pravara may be correct.