There is nothing wrong with using natural herbs to dye the hair or for other permissible purposes, so long as there are no harmful effects, because Allah, may He be exalted, says (interpretation of the meaning): “He it is Who created for you all that is on earth” [al-Baqarah 2:29].
It is not permissible to dye the hair black, for men or women, young or old, because of the general meaning of the evidence which indicates that that is not allowed.
The scholars of the Standing Committee for Issuing Fatwas were asked: I have seen some people using something to change the colour of their hair, whether they make it black or red, and I have seen them using something else to straighten curly hair. Are any of these things permissible? Do young people come under the same ruling as old people?
They replied: There is nothing wrong with changing the colour of the hair to any colour except black or with using something to make curly hair straight. The ruling is the same for young people as for old people. That is so long as there are no harmful effects and the substance is taahir (pure) and permissible.
With regard to changing the colour to pure black, that is not permissible for men or women, because the Prophet (blessings and peace of Allah be upon him) said: “Change this grey hair, but avoid black.”
End quote from Fataawa al-Lajnah ad-Daa’imah, 5/168
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: If the hair is dyed black, the Prophet (blessings and peace of Allah be upon him) forbade that when he enjoined changing grey hair but avoiding black, as he said: “Change this grey hair, but avoid black.”
There is also a stern warning addressed to the one who does that, which indicates that it is haraam to change the hair to black. As for changing it to other colours, the basic principle is that that is permissible, unless it is done in the style of disbelieving or immoral women, in which case it is haraam from that point of view, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever imitates a people is one of them.” Narrated by Abu Dawood, 4031; classed as saheeh by al-Albaani in Irwa’ al-Ghaleel, 5/109.
End quote from Majmoo‘ Fataawa wa Rasaa’il Ibn ‘Uthaymeen, 11/120
What is meant by the warning is the words of the Prophet (blessings and peace of Allah be upon him): “At the end of time, some people will dye their hair with black like the crops of pigeons. They will not even smell the fragrance of Paradise.” Narrated by Abu Dawood, 4212; an-Nasaa’i, 8/138; classed as saheeh by al-Albaani in Saheeh al-Jaami‘, 8153.
It is permissible to use the herbs mentioned to straighten hair, but if they give a deep black colour, it is not permissible to use for one who has some grey hairs.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked: Some people use a mixture to straighten the hair; this mixture is composed of henna and a number of other herbs, which includes a herb that dyes the hair black. What is the ruling on using this mixture? Please note that they are using it for the purpose of straightening the hair and not to dye it black, because some of them have black hair. What is the ruling on using it for a woman whose hair is black but there are some white hairs that are not due to old age, and she is also using it for the purpose of straightening her hair? Please advise us concerning that, may Allah reward you with good.
There is nothing wrong with using the paste mentioned to straighten the hair if the woman who is using it does not have any grey hairs. But when there are grey hairs, it is not permissible to use anything that will turn the grey hairs black, because the Prophet (blessings and peace of Allah be upon him) said: “Change this grey hair, but avoid black.”
End quote from Fataawa ash-Shaykh Ibn Baaz, 10/63
Based on that, if these herbs dye the hair black, and make it deep black as you say, then you should not use them.
And Allah knows best.