Firstlty, Dakinis and Dayans are completely different entities. The former are mentioned in many of the tantras, who are the Gannikas of Shiva and Parvati separately, while the later is from the Islamic expression and amalgamation in Sanatana over the period of time.
The, answer here covers following topics as asked by the OP-
Who are dakinis?
Are they good or bad?
How can an evil Dayan worship Mahakali?
How can Maa Kali be shown as chewing flesh?
My first question would be Who are Dakinis?
• As aforementioned, they serve Shiva and Parvati and accompany them in battles.
They (dakinis) can be seen in the Council of Devi standing with two hands folded in the Anjali mudra. Thus such female attendants are stationed in the puram (city) of devi.
Many other stotram describe devi as, Dakiniparisevita(The one served by Dakini), Dakiniparinutita (The one bowed down by Dakini),
Dakiniavruta ( The one surrounded by Dakinis).
While explaining the Shiv Avarana Pooja to Shri Krishna, Upamanyu mentions them,
Bhūtas, Ḍākinīs, Yoginīs, Śākinīs and evil witches, temples....
• They also, accompanied Veerbhadra and Bhadrakali devi to Daksha Yajna and many times with Devi to the battlefield.
• Dakinis are non other than expansion of the Devi herself.
Kali Sahasranaam calls out Mahakali as Dakini.
Also, Lalita Sahasranaam has her name as Dakini, there giving the hint that Dakini is none other than Devi herself.
Chinnamasta is flanked by Dakini and Varini devis on both sides. Here Dakini is considered as the embodiment of anger and Chinnamasta devi herself.
• Dakinis rules over the Vishuddhi Chakras in body as mentioned in Lalita Sahasranama.
Many would have already thought even the iconography of dakini devi something a similar to ghost shown in daily soaps. Thus, here is the Dhyan to clear the misconception.
Some of them have the complexion of Banduk Pushpa, some have a complexion of dark blue hue, some resemble gold in complexion, some to spatika, some reasonable to smoke while some to Champak Pushpa. They have fallen breast and huge ears with human head as the earrings. Their body is decorated with ash of the pyre, and appear fearsome. A half moon seen shining on their forehead. And a huge mouth can be seen with the huge tongue and teeths on the inner side. The hold many of the Astra Shastras, which may sum up to 24 in counting. When they dance all the three worlds tremble, thousands of lightnings spark in the sky and they set stars in astray.
Are they good or bad?
They are the entities that treat the way you treat them.
They are Kshiprasiddh devis (those who give boon very easily), only if done with a proper intention.
डाकिनी राकिनी चैव लाकिनी काकिनी तथा
शाकिनी हाकिनी देवी वर्णाना मंत्र देवता।
Dakini Rakini Lakini Kakini and Shakini Devis are the ruler deities of varnas.
गुणानाम् सिद्धि वर्णानाम् षडेते अधिदेवताह्।
O Parvati, these are the six ruling deities of Varna who gives Siddhi.
विना वर्ण परिज्ञानम् कोटि पुरश्चरणेन किम्।
तस्य सर्वं भवेद दुःखमरण्ये रोदा नं यथा।
Without the knowledge of the Varnas (six deities) the crores of purascharana will never fruitify.
And the Sadhak experiences torments similar to like crying in the forest.
ध्यायेच्छशिमुखीम् नित्या डाकिनीम् मंत्रसिद्धये।
Thus upon contemplating the moon like face of Dakini devi everyday, one attains Mantra Siddhi.
डाकिनी च महादेवि अणिमा सिद्धि दायिनी।
Dakini Mahadevi gives Anima Siddhi.
डाकिनी शाकिनी सत्व रूप ततः प्रिये।
O the loved one, dakini shakini are the Satvik forms.
सत्वरूपा...... एताश्चैव महादेवि चतुर्वर्ग ददम्ती हि।
The Satvik forms,.... Mahadevi gives the Chaturvarg (Dharma, Artha, Kama & Moksha).
They are referred to as bad ( as far as I know) Clarification would be needed.
Yes, they are the worst nightmare for those upasaks who tend to overlook the Shakti Upasana rules, and also for the enemies of the Devi sadhakas.
Those who chant the mantra by chanting every Varna differently, their Mantra is engulfed by Dakini.
Lalitopkhyanam, chapter 20 - The Deities on the Kiricakraratha,
Seven deities called Dhātunāthās were stationed in their respective places beneath the same step. They were Yakṣiṇī, Śaṅkhinī, Lākinī, Hākini, Śākinī, Ḍākinī and (another) Hākinī who had the united (and combined) forms of all of them. All these demonstrated the exploits of their mighty arms. They appeared ready to drink (i.e. destroy) all living beings and the Earth. They drank and consumed the seven Dhātus, essential ingredients, of the body (viz. the blood), skin, flesh, fat, bones, morrow and the semen of enemies. They had hideous faces. With their harsh leonine roars they filled ten quarters. They were called Dhātunāthās and they were the bestowers of eight Siddhis beginning with Aṇimā (minuteness).
Thus, if any of the Dhatunathas if charged on anyone, they can kill them. Or if one chants wrong mantra the Dakini devi eats that mantra. Thus, sadhaka can't accumulate any mantra urja.
At times Dakinis get notorious by themselves and harm someone.
Thus, Chandi Kavach wards them off,
डाकिनी शाकिनी..... नाश्यंती दर्शना तस्य कवचे ह्रदी समस्थिते।
Dakini shakini.... will be banished upon seeing the person who wears the Kavach in the heart.
How could a Dayan worship Kali ma who burns Evil spirits just by reciting her name??
Firstly, as I said, dakinis are not to be taken as Evil entities. Even if tho someone consider them to be as evil as they get mischievous at sometimes then also one must highlight the fact that, Maa Kali is not Human who is going to think what is right or wrong and on that basis she will decide what to do next.. Nothing like that.
Kali is Para Chiti Paratpar Param Brahma, she is neither Partial nor creul.
Brahma sutra 2.1.34
वैषम्यनैर्घृण्ये न सापेक्षत्वात्तथाहि दर्शयति।।
Same is in Gita 9.29
समोऽहं सर्वभूतेषु न मे द्वेष्योऽस्ति न प्रिय:
I am equal for all living beings; I am neither inimical nor partial to anyone.
Thus, every entity has a right to serve her.
Remember, she is the same Chamunda who was protecting Ravan because he had done the Sadhana to please her, and she is the same devi who gave the boon of victory to ŚrīRām.
Thus, she is impartial to everyone.
Shri Shankaracharya says:—
The Lord is to be looked on as analogous to that of Parjanya, the Giver of rain. For as Parjanya is the common cause of the production of rice, barley, and other plants, while the difference between the various species is due to the various potentialities lying hidden in the respective seeds
How could Kali ma be referred to as "eating flesh" ?
Because Shastras say so.
Some of the forms of Mata Kali actually eat flesh. Such forms are not open for everyone as they are not benevolent like mothers and may be cruel in nature.
For example Shamshan Kali, as per dhyan is seen as,
She is dark in complexion, and her hair disheveled. Her eyes are bloodshot and Her teeth is terrifying. Her body is gaunt and unclothed. She sports a long lolling tongue. In her left arm she carries a Kapala (bowl made of skullcap) containing blood, wine and meat. In her right hand she holds a decapitated head, from which blood is flowing. She is chewing on human and animal flesh constantly and rides in a cremation ground.
Thus, altough Bhakti is must and it is great to view Mahakali as mother. But, do not let Bhakti overwrite Shastra.