This is the transcribed Will of Thomas Buckner of Westhampnett, Sussex, England, 1704 (LDS microfilm #0194588 p. 698, Consistory Court of The Bishop of Chichester)
Thomas Buckner is fairly well recorded in Sussex documents. He had previously lived in Walberton, and married, probably as his second wife, Frances Moorey, a widow of Boxgrove who was the daughter of Henry Covert. A 1677 christening record for his daughter Elizabeth indicates that his first wife was named Elizabeth as well. The son Thomas seems to have married Elizabeth Dyer in Oving, Sussex in 1707. One child of Thomas Jr., Betty, is recorded in christening records from 1709 and died in 1710. My suspicion is that Thomas Sr. was the son of John Buckner who was recorded in a protestation return for Walberton in 1641/2 and similarly appears in a few scattered records of the area. There are two marriages, one to Anne Taylor on 4 July 1643 and a second to Anne Sander (or "Gander") in 7 Aug 1655. Three burials also appear, Emlin d.o. John on 20 Mar 1654, Mary Buckner d.o. John on 30 Apr 1655 (who was christened 6 Jan 1644), and finally John Buckner on 1 Dec 1657, which is probably his death.
We can connect Thomas of Westhampett to Walberton via christenings there for Mary (24 Jun 1675), Elizabeth (20 Feb 1676), and Thomas (3 Mar 1679), children of Thomas and Elizabeth Buckner. Since the names of the 3 children are identical to the 3 in the will, the identification seems conclusive. Thomas Sr. married Frances Moorey in Chichester on 27 Dec 1687, so she was probably his second wife.
One of the earliest Buckners in southwest Sussex seems to have been Hugh Buckner of North Mundham whose modest estate of 25-odd pounds was administrated by his widow Anne in 1629. John Buckner was a witness to the will of Henry Chatfield of North Mundham on 28 Jan 1636. It seems fairly likely that John was Hugh's son. Thomas Buckner Sr. was probably born in the 1640s or 1650s, so he may have been a son or grandson of this John Buckner. There is in fact a christening of a Thomas "Buckner or Bucknam" son of John in Walberton recorded on 6 Jan 1647, which would fit pretty well with this. I think we can firmly conclude that Thomas of Westhampnett was the son of John of Walberton, but beyond that, the connections are still tentative.
Some other things from North Mundham parish records include unnamed "Bucknar" burials on 8 May and 3 Oct 1629 (presumably one of them of Hugh), burials of John's children Joseph (3 May 1630), William (3 Mar 1632), and Francis (22 May 1638), and an unnamed Bucknar burial of John's spouse on 12 Apr 1640 (either Spring is when the ground thawed or it was a very unsalutory season in North Mundham). We also have a christening of Dorcas "Bucknet" d.o. John on 18 Feb 1626, as well as christenings of William, Joseph, and Francis. I should also mention the 1560 burial of a "John Buccer". Obviously, if this last is actually a Buckner, it complicates the story a lot though. One should note that there were quite a few Buckners in Kirdford, Sussex, too in the early 1600s. As a very vague hypothesis, I think the situation might have been that John Buckner Sr. was the son of Hugh Buckner and that they moved to North Mundham from Kirdford not long after John Sr.'s (second) marriage to Frances Madewick in 1622, which is why we have a namesake daughter Frances in North Mundham. John Jr. was probably thus the John son of John christened in Kirdford in 1623, which would fit well with the apparent age of John Buckner of Walberton.
I've tried to preserve the line arrangement so anyone who wants can compare this to the original image. I don't claim perfection, and there are some things that can be interpreted different ways.
Date of will: 29 Aug 1704
Probate: 4 Nov 1704
People named in the will:
In the name of god Amen The nine & twentith
day of August in the year of our Lord 1704 I Thomas Buckner of the
parrish of Westhampnett in the County of Sussex yeoman being very sick and
weak in body but of p{er}fect mind & memory (thanks be given to God therefore ~
calling unto mind that mortality of my body and knowing that it is appointed for a
man once to die Doe make and Ordaine this my last will and Testament (that
is to say) principally & First of all I give and recommend my Soule into the
hands of God yt gave it & for my body I recommend it to the Earth to be buried
in a Christian like manner at the discrecon~ of my Executor hereafter named
nothing doubting but at the generall Resurreccon~ I shall receive the same
againe by the mighty power of God And as touching such worldly Estate wherever
it hath Pleased God to bless me in this Life I give devise and bequeathdispose
of the same in the following man~er & Forme Imprimis to my Loving wife
Frances the Interest of Four score pounds att pounds[????] I give to her during her
naturall life & Alsoe ye use of all my household goods during her nr~all life
Item I give to my Daughter Mary the sum of twenty pounds Item I
give to me Grandson Thomas [T?]owning the su~me of Five pounds which said su~me of
Twenty pounds to my Daughter Mary & Five pounds to my Grandson Thomas
before menc~oned to be paid respectively in One month after my decease and my said wife
Frances And the said moneys to be put into the hands of Mr Heberden of East
Lavant soe that the Husband of my said Daughter may not have the Wasting
of itt but that Mr Heberden may deale itt to the p{ar}ties abovemenc~oned as neede
shall require Item I give to my Daughter Elizabeth the su~me of Fifty pounds
to be paid out of the money in Mr Reason's hands^Item I give more to my
Daughter Elizabeth after the decease of me & my wife The bed with green
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Curtains & the other appu~te~ces belonging to [smudged] bed & also six pewter dishes [?]
the least bell[?] mettle pott Item I give to my beloved son Thomas Buckner my house
at Midhurst that is Burgher holding after the decease of my Loveing wife
enjoyning my said wife to keep it in good repair during her nr~all life LAstly
I constitute my beloved son Thomas Buckner my full & sole Executor of this
my last will and Testament Alsoe I give to my son Thomas all moneys on bond
or otherwise Excepting that moneys in Mr Reason's hands Also I give my C[?]
Stock to my said son Thomas towards the defraying my Funerall Expenses and
I doe hereby revoak all Former wills & Testaments Ratefying & confirming
this & not other to be my last will & Testament In Witness whereof I have
hereunto sett my hand & Seal the day & year above written The mark of
Thomas Buckner Signed sealed published pronounced & declared by the said
Thomas Buckner as his last will & Testament in the p{re}sence of us the
Subscribers viz {MARK} Charles Collins John Huffman hismark Thos. Hammond
Probatum fuit hu[noi~] Testum~ Cora~ Ven~ Viro Thoma Briggs
Legu~ Dcore Vicario & Quarto die Novembr~ 1704 Iurament Thoma Buckner
filij nr~alis l~timi dict defunct ac Ex~oris ut Cui &c de bene Iurat salve &c