What type of sealent do you recommend for healing thick branches if I prune?

I have one but I think it is not suitable for figs because it flows away from the wound and does not cover...

Natural latex.
There is plenty of latex inside of fig branch, when you cut or pinch than the drop of fluid comes out of cut and seal the injury.
So answer is none, fig tree do it itself

But if I make grafting it always get rot under the parafilm...

Panache привиты мужской инжир, весной 2016 года парафильмом используя 2 года, очень доволен результатами. https://www.facebook.com/photo.php?fbid=799916350095694&set=pb.100002320080230.-2207520000.1476278859.&type=3&theater .

My parafilm is from a lab shop from Hungary. One roll is around 10k Forint ($40). So 100% original...

It is not the problem of the Parafilm but the wood always rots under it.

If I make thick cuttings the latex will flow even after 2 weeks...

Vinny,

Even when we prune in the winter cutting large diameter branches and leaving them unprotected creates all sorts of problems in large adult fig trees due to the excessive humidity and rains entering the open wound.
I always protect the largest diameter cuttings to avoid that and still have a few problems with excess humidity entering the trunk and causing tissue disintegration in older trees like in the following 2 photos:






Helike,

To avoid problems due to excessive latex inside the parafilm, make a few superficial cuts below the graft.

The cuts should be superficial but deep enough to reach the vascular tissues. This allow for the excessive latex to escape the branch you are going to graft.

You can do that some time before the graft if the tree has a great flow of sap or minutes before if the flow is medium. This avoids the drowing of the graft.
The growing bud will break the single layer of parafilm and allow the excess moisture to escape avoiding the accumulation of moisture inside the parafilm and the rotting of the graft.

In the winter months, with dormant buds i always cut the parafilm after the graft has taken (usually 4-5 weeks after doing the graft) to avoid rotting and fungus growing underneath.

Jamie,
Ok I agree with you, I was talking about pruning not chopping down a tree lol. I think Fig trees are tough unlike other fruit trees fig trees will bounce back as suckers. I'm my weather if pruned in early winter the cuttings have more chance to root well but not necessarily good for the mother tree itself. I think for the benefit of the mother tree and to get quality cuttings late winter to early spring is the best time. About making such huge cuts I think its better to wait till the tree goes fully dormant and I mean like in the coldest month . I have seen people uprooting and burying whole Fig trees in Canada for winter, but this may not work in your beautiful climate.
About this parafilm you are right. I had no moisture issues after making superficial cuts and I can say that I only lost one graft out of few grafts last year and it was because the rootstock died. Girdling with a metal wire also helps .

I've used some Japanese Bonsai/tree sealant that worked well.
http://m.ebay.com/itm/Bonsai-tool-New-Kiyonal-Tree-Wound-Sealant-Cut-Paste-100-gram-/201574803536

A great sealant is "liquid Tape". I have used it a lot and it works outstanding and dries fast!

I know some old timers who use Elmers Wood Glue.

liquid electrical tape

I use Elmer's glue just like Coop mentioned... You can do a thin layer or just lay it on thick...