Is it real?
This website of dvaita argues that it is real.
In footnote 49 on page 39, and elsewhere, Mesquita calls a Sruti text of Madhva with the label Paingi unknown, following Appayyadiksita. In fact:
In the Kasika commentary8 (pp. 192-193) on Panini's Astadhyayi 4.3.105, we find the statement kalpesu paingi kalpah, showing that this was an important recension with its own Kalpa-sutra. Patanjali's Mahabhasya on 4.2.66 also refers to the same, and indicates that said Kalpa-sutra was actually available to him: evamapi paingikalpah atrapi prapnoti.
A manuscript of a Paingayani Brahmana is reported by Oppert9 (p. 22, no. 390) to have been in the possession of one Venkatarama Srauti of Mullandram. Also see pages 454, 557, and 582, where Oppert notes other manuscripts. Therefore, in all, Oppert reports a total of four manuscripts, although there do not seem to be more recent reports of them (a matter unfortunately not helped by the fact that Oppert's catalog does not give any accurate contact information on his informants).
Paingi Grhya (further evidence of a robust recension) is quoted by these10 (pp. 187, et seq.) traditional commentators--Haradatta on Apastambha Grhya 8.21.9, Maskari on Gautama Dharmasutra 14.6.17; the Paingi Dharmasutra is quoted in the Smrticandrika (Asaucakhanda).
Paingi is counted as one of the Sakhas of the Rg Veda by the Prapancahrdaya,11 a pre-Ramanuja text, in its second chapter (Veda Prakarana).
Teachers of the Paingi clan are quoted in numerous pre-Madhva texts, e.g., Sankhayana Brahmana 16.9; Patanjali's Samavediya Nidanasutra 4.7; Brhadaranyaka Upanisad 6.3.10 (Madhuka Paingya is mentioned).
The Paingayani Brahmana is twice quoted in the Apastambha Srauta-sutra (at 5.14.18 and 5.29.4).12
There are literally dozens of citations from Paingi, Paingayani, and Paingala Brahmanas which have been collected by Satya Shrava, pp. 45-48,13 and by Ghosh.14 For brevity, we do not list them all here.
A Paingi-Sruti (having an Upanisadic flavor) is quoted by Sudarshana Suri (a disciple of Ramanuja) in his Srutapradipika, as well as in the Srutaprakasika in the catuhsutri portions. These are the same as that quoted by Sankaracarya in his own commentary15 on the Brahma Sutras, but SS quotes a few more words. Thus, early authors from the other two Vedantic streams also cite this source.
Shankara references Paingi rahasya brahmana in his brahmasUtra bhAshya 1.2.12 and 3.3.24.
………अपर आह — ‘द्वा सुपर्णा’ इति नेयमृगस्याधिकरणस्य सिद्धान्तं भजते, पैङ्गिरहस्यब्राह्मणेनान्यथा व्याख्यातत्वात् — ‘तयोरन्यः पिप्पलं स्वाद्वत्तीति सत्त्वमनश्नन्नन्योऽभिचाकशीतीत्यनश्नन्नन्योऽभिपश्यति ज्ञस्तावेतौ सत्त्वक्षेत्रज्ञौ’ इति………
………अस्ति ताण्डिनां पैङ्गिनां च रहस्यब्राह्मणे पुरुषविद्या ; तत्र पुरुषो यज्ञः कल्पितः ; तदीयमायुः त्रेधा विभज्य सवनत्रयं कल्पितम् ;
Is anything from it quotable
Shankara does mention its contents in the two places mentioned above.
The highlighted line below is a translation of a quote from the paingi rahasya brahmana.
Another (commentator) gives a different interpretation of the mantra, 'Two birds inseparable,' &c. To that mantra, he says, the final decision of the present head of discussion does not apply, because it is differently interpreted in the Paingi-rahasya Brâhmana. According to the latter the being which eats the sweet fruit is the sattva; the other being which looks on without eating, the individual soul (gña); so that the two are the sattva and the individual soul (kshetragña). The objection that the word sattva might denote the individual soul, and the word kshetragña, the highest Self, is to be met by the remark that, in the first place, the words sattva and kshetragña have the settled meaning of internal organ and individual soul, and are in the second place, expressly so interpreted there, (viz. in the Paingi-rahasya,) 'The sattva is that by means of which man sees dreams; the embodied one, the seer, is the kshetragña; the two are therefore the internal organ and the individual soul.'
In the Rahasya-brâhmana of the Tândins and the Paiṅgins (the Khândogya) there is a vidyâ treating of man, in which man is fancifully identified with the sacrifice, the three periods of his life with the three libations, his hunger and so on, with the dîkshâ, &c. And other particulars also are mentioned there, such as formulas of prayer, use of mantras and so on.