Grading: Its chain is weak.
Technical note / Defect ('illah): The narrator "Abu Yazid al-Dinni" is majhul (unknown). Imam al-Bukhari said (as in al-Tirmidhi's al-'Ilal al-Kabir 201): "Abu Yazid, I do not know his name, and he is an unknown man." Al-Daraqutni said in "al-Sunan" (2271): "He is not known." Isra'il (in the chain) is "Ibn Yunus al-Sabi'i".

Reference / Source: Ahmad (45/27624), Ibn Majah (2531) and al-Nasa'i (4893) narrated it by two routes from Isra'il, with this chain.

Reference / Source: 'Abd al-Razzaq (13867) and Ibn Abi Shaybah (12685 - 'Awwamah) narrated by way of Ma'mar, from al-Zuhri, who said: It reached me that 'Umar bin al-Khattab (may Allah be pleased with him) used to say: "To give someone a pair of sandals to ride on in the path of Allah is dearer to me than freeing a child of zina."
Grading: Besides the "inqita'" (break) between al-Zuhri and 'Umar, this narration is "mawquf" (a saying of a Companion).

Important point: The marfu' hadith of Abu Hurayrah (may Allah be pleased with him) has already passed with the author at number (2912): "The child of zina is the worst of the three (the mother, the father and the child)." Abu Hurayrah said: "That I give someone a whip to use in the path of Allah is dearer to me than freeing a child of zina." See narration (2914) and the words of Lady 'A'ishah (may Allah be pleased with her) after it.

Reference / Source: 'Abd al-Razzaq (13860) narrated by way of 'Urwah, from 'A'ishah, that whenever it was said to her "He (the child of zina) is the worst of the three", she would disapprove of that and say: "He bears nothing of the sin of his parents; Allah says: ﴿وَلَا تَزِرُ وَازِرَةٌ وِزْرَ أُخْرَى﴾ [No bearer of burdens shall bear the burden of another]."
Grading: Its chain is sahih.

Note / Clarification: This narration will come with the author at number (7230) as "marfu'", but its "raf'" (attribution to the Prophet (peace and blessings be upon him)) is not authentic.